Disregard everything I've said - I've discovered that the Google Play version through Aurora allows me to toggle Notifications, but the F-Droid version via the Droid-ify repo doesn't. I will report this issue to Bitwarden and will use the Google Play version for the time being.
(However, I'll still keep my previous post for the sake of record keeping in the case anyone else has this same issue.)
Thank you for helping me work through this!
unwat Also, just as a side note, I have set up log in with device on my own Bitwarden account, but I never get the notification. The only way I can get it to work is by launching the app and refreshing my vault.
I this this is somewhat expected, because Aurora Store says that Bitwarden requires GSF, so any push notification related activity more or less only works on GOS with Google Play Services (and I'm conjecturing YMMV even if you installed the sandboxed Google Play Services). I know this from experience with Keybase, Proton Mail, and Wire (before it was distributed directly on F-Droid, and I'm not sure now since I've basically stopped using Wire since 2021).