What would be a good way to backup the passwords stored in Bitwarden? I am worried that someday suddenly bitwarden could stop working and I will lose access to all the stored passwords? Should I have a physical copy of all the passwords stored in a vault at home?
The simplest way of doing this would be to export your bitwarden vault in plaintext (as a json or csv) and then store it as a password protected zip file.
This should be easy to encrypt and decrypt on all operating systems, and would make it easy to move your vault to a new password manager.
If you have some sort of home server, I'd recommend hosting vaultwarden (an open-source implementation of the BitWarden server). It works fine with the official apps. Their enterprise model requires a standard API, so it's not going to break anytime soon.
This does not take the need for separate backups way though. In fact, I'd argue it makes it even more important to maintain a 3-2-1 backup of your vault.
Running vaultwarden on a home server is one small disaster away from losing everything. Homelabs typically don't enjoy the same level of protections and redundancies compared to a commercial DC.
Use the export feature and just save the file somewhere safe, mine is in a Cryptomator vault. You could also import to Keepass and then delete the file.
Frankly I would worry about that with any third party that holds my data. There are a few Bitwarden exporters on Github that also account for attachments (something the builtin exporter doesn't for some reason).
BW synchronizes all your data on each client... if you logged in before, and your server goes down, you can still log in to a recent client, it just won't be able to update
