I can confirm what MotherShipton and DeletedUser639 already stated:
I have tried several alarm sounds and can confirm that the standard sounds work in BFU - also with vibrate toggled on.
However Clock> 3 dots> Gradually increase volume activated caused some issues with other than the default alarm sound: The alarm seems to go off - you see the blue clock screen - but you can hear no alarm sound or only a very quiet one not increasing its volume.
I briefly tested it and the issue is still present on build 2026021201.
Edit: ejns was faster than me, didn't see his post:
I did some testing and found that if you use the 'gradual volume increase' for the alarm, it will sound silently in BFU state. Turning that setting off allowed the alarm in BFU state to be sufficiently loud.