I just got the update on my phone on Google play, Firefox now supports 3rd party password managers for passkeys (on android 14+). Just tried it, and I got prompted with my 3rd party password manager, so it works!
For people using Nightly. Bitwarden as of yet does not have the package name for Firefox nightly in its allow list. So you gave to switch to either Firefox beta or as mentioned here Firefox for it to work.
The passkey function doesn't work with 3rd party password managers anyway, unless you use Android 14+ (I think, maybe even 15). Otherwise the Google default tries to handle it.