Hi. I’m sorry that I can’t provide a solution to your issue, but I can confirm that I have the same problem on a similar set-up as Yours (RPi4 + Home Assistant OS 6.1 + core-2021.7.3 + supervisor-2021.06.8)
and I have found a temporary work-around.
This is what I have identified so far:
If I log in with my user on any device (PC with browsers Firefox or Edge, Android official app or IOS official app) I get a working dashboard just as expected.
However, any additional user that I have created via Configuration->People in the Lovelace GUI, will end up getting a “blank” dashboard. Or, almost blank. They get the title bar on top (with the correct dashboard name), but there are no visible cards, ie. not so useful.
So, what’s the work-around, you may ask? When a secondary user (with admin rights) logs in, they can still access the “three dots” menu at the far right of the title bar. There they select “Edit dashboard” and are presented with the edit mode (darker title bar, some additional icons) but still an empty area where the cards are supposed to be.
Here they click again on the three-dotted menu, and select the “raw code editor”, and boom - they see all the code behind the cards. At this moment, all they do is to click the X exit button at the far left of the title bar twice, and everything is back to normal - as you would expect it to look and function.
Thing is, that once that user logs out it’s all lost. They have to do this procedure all over again on their next login. I don’t have to tell you what that does to the “spouse factor”… 
My guess is that this behaviour is related to some set-up or general configuration that I have missed or accidentally skipped. If anyone can see and point to the flaw, it would be much appreciated.
PS. Also found this related post, but no further help/explanation to the issue:
https://community.home-assistant.io/t/blank-dashboard-for-second-user/270568
Update 2022-02-04:
By chance I seem to have solved the issue while troubleshooting one of the iOS devices not updating it’s location properly. After doing the (now usual) “raw code editor” -magic mentioned above, I swiped down on the main screen to force a sensor update. And that solved the missing location for that user, but see and behold - next time I opened the app, I was presented the correct dashboard as well! Hopefully this will also work for that android device that’s been bothering me, but it will be a couple of weeks until I can try it out. (It’s currently at a boarding school far from home 
)