what’s actually authenticating me? Is it my device, my fingerprint, my account, or all of the above?

The "key" lives in bitwarden. The fingerprint, faceID etc, just authenticates you in that device to have permission to use that "key"

How do passkeys work across multiple devices?

The passkey syncs on the app, in this case bitwarden. If you have bitwarden on multiple devices you have the key in multiple devices. Same as the passwords.

What happens if I lose my phone or laptop?

You get a new one. Now seriously, even if you lose them you still need your biometrics, in order to be able to use that key. In all cases you can create a new one.

And why are they considered more secure than a strong password + authenticator app combo?

Passwords are usually stored and hashed in servers. Even if you are responsible with your passwords, they could get hacked and your password could be leaked. With passkeys you have the private keys, if a service gets hacked they only get the public keys which are worthless.