HA is running on RPi 4 (past 6 years), no issue with Bluetooth until latest update. I only have a few devices using Bluetooth - two of the fairly recent Switchbot presence sensors, and a few plant sensors. There are also 2 Bluetooth proxies running on ESPHome atoms.
If I reload the integration Bluetooth comes back on for a random amount of time, a few minutes if not longer.
The only thing in the logs (core) is of the plant sensors Xiaomi going offline. I have checked all logs under system and there is nothing apart from the plant sensors being mentioned, nothing about the Bluetooth integration.
Device: Raspberry Pi Trading Ltd bcm43438-bt (E4:5F:01:0E:A0:9B)
Sometimes the Bluetooth radio can end up stuck in passive scanning mode, although I usually get a notice about that when it happens. Anyway, you might try powering down the Pi, unplugging it for 10 seconds, and then powering it back on. When I get the notification about the issue, those are the instructions, and that tends to fix it for me.
I noticed this too, but I thought it was just my complicated 2.4ghz Apt / Flat environment. Lots of neighbors with lots of devices in a small area.
In my troubleshooting I noticed my BT RSSI values weren’t as good as I thought they should be, so I lowered my AP’s 2.4ghz power from 100% → 50% and the RSSI values improved, and the disconnects are reasonable.
I don’t know how to check what BT channel HA is using, but I assume for whatever reason in my case it is or was close to my 2.4ghz wifi channel.