You should definitely be! I take backups every 6h for my self hosted vaultwarden (easier to manage and to backup, but not official, YMMV). You can also restore each backup automatically and have a "second service" you can run elsewhere (a standby basically), which will also ensure the backup works fine.

I have been running bit/vaultwarden now for I think 6 years, for my whole family and I have never needed to do anything, despite having had a few hiccups with the server.

Don't take my word for it, but the clients (browser plugin, desktop app, mobile app) are designed to keep data locally I think. So the term cache might be misleading here because it suggests some temporary storage used just to save web requests, with a relatively quick expiration. In this case I think the plugin etc. can work potentially indefinitely without server - something to double-check, but I believe it's the design.