From Bitwarden’s Passkey FAQ:
…Passkeys are often able to sync across your devices, however not all platforms support this yet. …
Do I use the same passkey regardless of the browser I’m on or will each site require a different passkey depending on the browser or device?
The passkeys stored in Bitwarden are synced passkeys, meaning that any browser where you are logged into the Bitwarden extension or where you have the Bitwarden mobile app installed, you can access your accounts using the same passkeys without needing to create new ones. If you don’t store your passkeys in Bitwarden it will depend on how well the browser integrates with your device OS (where the passkeys are stored).
Bottom line, though, Passkeys remain a “work in progress” both within Bitwarden and industry-wide. Support for them is nowhere near universal, and there are often variations in how they behave from site-to-site.