I have one of them I bought in a Grilplats and Bilresa bundle. The Grilplats works amazing i just bought as an extender and the button because it was only $4 CAD extra. I put one of the buttons by my nightstand. That was sticking at 14% and rejecting the update basically. There is a firmware issue where the battery sensor is also broken and it can’t update. This seems to be a firmware and chip error. Same story, I updated to the newest Home Assistant OS, got a update, attempted to install, failed. If you have this issue you can: Contact IKEA online by their chat for a defective product. Ensure you have your receipt or if you used a IKEA Family Card you can view the purchases online to get the receipt number. IKEA will send replacement units free of charge to your house or offer refunds by gift cards. You won’t have to send back the item. Contact for IKEA page: https://www.ikea.com/ca/en/customer-service/knowledge/articles/c9c260c7-69e3-43cd-82f0-f96f20b2g519.html
It took about 2 hours of babysitting retries to update my 5 switches. I would LOVE an option in Home Assistant to auto-update, or at least to automatically keep retrying to update on its own.
I have updated 2 and it required that I disable the automations I have associated with them and then hitting the button over and over for literally 20-30 minutes to keep it awake. I have 6 more to update. I will try some of the methods mentioned here next. Good times! All the rest of the IKEA Matter devices have updated fine (water sensor, door sensor, air monitor, and temp sensor).
The motion sensor has a similar issue to the Bilresa remotes though. Still haven't been able to get it to update.
What about giving the "Zen" Method a try?: click the udate button turn away and focus on something more important in your life.
After an hour or so you might re-check if it succeeded or not. But i can't imagine that hitting any buttons during the update process is doing any good. Thread is teaching us patience! In Thread we trust ... 
Ikea (and their subpar subcontractors), not Thread. I've got Thread devices from three different vendors (Eve, Aqara and Ikea) and it's only the Ikea ones that are really troublesome (Eve gives me no issues whatsoever, Aqara once a quarter, Ikea every week :)).
FWIW, my two Bilresa buttons took a whole evening to update. The Klippbok sensor took a few minutes.
I was able to start updating after I changed the channel thread ran on.
I moved it from the default 15 to 26 and updates worked.
To do this, Settings > Thread > 3 dots for the thread network > Change channel.
Okay, but both channels (15, 26) are usually not optimal. You might want to look at your WiFi channels and also at the usage of Bluetooth devices. Here is a nice chart that shows the overlapping and free channels of WiFi/Bluetooth and Zigbee/Thread:
In general: when you keep your WiFi Router set to US-Scheme and only use channels 1,6 or 11 in 2.4 Ghz with Bandwidth limited to 20 Mhz, you can safely use channels 20 and 25 (orange marked) for Thread or Zigbee without getting interferences with your Router (green marked) and Bluetooth devices (blue marked).
I have 8 Bilresa dual buttons that I have been trying to update for over a week. None have succeeded. Most of the time, HA just shows "Installing". On occasion, it has progressed a few %. One time, I think it event went to 49%. In all cases, the update failed. Between all 8 buttons, I have probably made well over 100 attempts. I tried to bring a button near the ZBT-2 antenna, and press one of the buttons during the update to keep it awake. It did not help.
I've got 7 Bilresa dual button switches.
4 of them updated at the first attempt directly from the Matter Server app web UI.
2 failed, became unresponsive, and had to be reset and re-paired before then updating properly.
1 failed, but still works. It now refuses to even start the update.
On top of this, I'm still getting random dropouts on several Kajplats GU10 lightbulbs, while others are rock solid.
It's a shame you can't "re-interview" devices using bluetooth to bring them back online.
I have all but 1 remote updated (out of 8). Just kept trying until it installed. Hopefully this firmware issues fixed some of these issues and the next update won't be as painful. (Wishful thinking).
Update: They all finally updated. I just kept trying. The door sensor came in yesterday with an needed update and it took a couple attempts as well.
I tried switching to channel 20. No luck.
I don't have any bluetooth devices. I do have 311 IOT clients on 2.4 GHz bands, on non overlapping channels 1 / 6 / 11.
I can't get any of my 8 Bilresa to update. I'm not sure if it's the wireless signal or something else.
Other low bandwidth devices - 126 Z-wave/Z-wave LR and 110 Yolink LorA - are always able to update firmware properly, even it takes a while. The slowest I have ever seen is a non-LR Z-wave device taking a few hours. A few may not have installed the first time, but it never took more than a couple of attempts. Z-wave and Yolink use lower frequency bands, though, not 2.4 GHz range.
These Bilresa / Thread devices on 2.4 GHz really are something else.
Since the Thread network is known to be low bandwidth, there should be a reasonably long timeout. I suspect it is a timeout issue, but have no way to prove it.
The button functionality itself works, so wireless signals are definitely getting through. I had to install 5 Grillplats mains-powered smartplugs as repeaters to get the buttons to work in the locations I needed them to. The repeaters haven't gotten a firmware update yet. It would help if they did, to see if the problem is specific to battery powered devices or not.
Did you try to put the Bilresas close to the TBR, or a router device like the Grillplats, just to see if it's a radio connection problem? Due to their magnetic mounting, it should be easily done.
If the update process works better close to a router device, then it's the proof that your mesh is insufficiently stabilized and you are gonna need more routers in your thread mesh.
I can only recommend to use the beta version of the Matter Server App and beta Version of the Open Border Router App as well. At least in my Thread Mesh they both work pretty good and might solve some of your problems, if they are not caused by clients being positioned too far away from routers.
No, it does not work any better next to the Grillplats, or to the ZBT-2. It always fails. Even if I power cycle it (pull/reinsert battery) to force it to reconnect.
I'm using the beta Matter server app already. I just switched to the beta Open border router app.
It's been stuck at "installing" for several minute without progressing to 1%. I don't expect it will make a difference, but I'll report if it does.
I don't think the distance is the problem given that HA receives the signal from the buttons successfully even in their intended locations. The fact that moving them closer also doesn't help points to it being a different issue than distance.
Edit:
The Matter server Thread display does show abnormalities for 3 of the Grillplats.
I have no idea which one is which, though.
Some progress.
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I was able to find the Bilresa and Grillplats Node ID in Home assistant under Settings/Devices/Matter/device name. The "Matter info" doesn't initially populate. It takes a few seconds for it to display. Then, I have to click on it. Finally, the node ID appears.
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In the Matter server GUI, I was able to update the node name by clicking on Node / Endpoint 0 / Basic information / Node label . I did so for all 5 Grillplats and 8 Bilresa.
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I then was then able to get a more useful network view.
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I could still not update anything.
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Since it's now, daytime and lightbulbs are not needed, I flipped the relay to off on the 72 Z-wave light switches. This powered off 221 Wiz light bulbs, which would have reduced utilization on Wifi channels 1, 6 and 11. This should have had no effect on the Thread network on channel 20, as its spectrum does not overlap with these Wifi channels.
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Nevertheless, I was then able to successfully start the update on one of my most distant Bilresa, which is behind 2 Grillplats repeaters, without having to move it. It took about 10 minutes from start to finish.
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I have still had no luck getting any of the other 7 Bilresa to move past the initial "Installing" state.
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I pulled and reinserted the battery on some Bilresa in an attempt to force them to reconnect to the nearest repeater. The reconnection worked. However, the Node label configured in step 2 was lost.
For some reason, I can’t even get mine to 1 percent. My update fails a few seconds after starting, even before reaching a percentage. I have every single Thread network device online. I don’t know why it instantly fails.
How long did you wait after clicking "update"?
What exactly did it show, that made you think it failed?
My impression is that you click it once and then best stop observing it, turn away, let it do it's thing and come back half an hour later.
That's how ALL of my Ikeas finally updated themselves successfully.
I had the same issue. Strangely after I changed from python-matter-server to the "newer" matter.js based matter-server it worked just fine?
No idea if that helped in any way.
edit Haha nope! Wishfull thinking. Still seems like it is just a question of continuously restarting the update until it succeeds...
I managed to update mine by pressing the buttons, alternating, every 2-3 seconds when it was updating. To prevent it from sleeping?
The new Matterjs server has several optimizations to help with Ikea specific hardware/firmware oddities. Still an expertise in patience, but the isssue is the specific hardware ikea choose and the fact that the device, by early design restarts 2-3 times during these early firmware updates. Most matter controllers just give up and assume the device is no longer available.
I just tried the suggestion to change thread to channel 26 (was 15) and it worked for my three Bilresa remotes. They are now on 1.9.15.
I am on HAOS 18.0 OpenThread 3.0.1 and Matter Server 9.0.2. Thank you everyone for your help.