I have this exact issue too. I have the same phenomenon in both Safari and Brave browsers (haven't tried others). It appears (to my uninformed self) that Mac OS is probably blocking Alfred when in a password field, but there's then a second phenomenon whereby even after shifting focus / tabs, the hotkey (Cmd+space) doesn't activate Alfred.
However, if I 'toggle Alfred' from the menu bar TWICE (presumably once to turn the invisible instance off, and then once to turn it back on again), it reappears, and my hotkey works again. In fact, if I toggle it off using the menu bar, I can summon Alfred with Cmd+Space, as usual.
Interesting re: Apple Watch. I'm using an Apple Watch to unlock, although I tried locking the Mac and unlocking with TouchID and the same things happened. Perhaps if restarted and logged back in again without using my watch it might be different, but the fix you mention doesn't seem to help. Also the same with/without BetterTouchTool running.
To be honest it's not a major issue for me. It's just a weird bug.
I get the Console message above, and also this one:
Since sending application [sess=100005 pid=903 uid:501,501,501 g:20,20 pV:2298] is not permitted to send this AppleEvent to this process, returning an errAEEventNotPermitted reply.
Alfred 4.6.1 [1274], no powerpack
MacOS 12.0.1
Safari Version 15.1 (17612.2.9.1.20)
Brave Version 1.32.113 Chromium: 96.0.4664.45 (Official Build) (x86_64)
2018 MacBook Pro 13" w touchbar