It would be great to be able to use Bitwarden as a system-wide password manager, though it probably makes sense to create it as a separate service which talks to the remote REST API.
It would definitely be amazing if the Bitwarden desktop application implemented the https://specifications.freedesktop.org/secret-service/ service so that all the Linux applications that use this interface can store/retrieve passwords/secrets could use Bitwarden. (On most systems the interface is usually implemented by libsecret/gnome-keyring)
Yes, I just came here for the same, my use case is to also be able to use bitwarden as a credential helper for git.
As example of dbus API implementation, we can lookup links to commits in Make KPXC databases accessible via libsecret/DBus KeePassXC issue, that implement this feature recently in 2.5 release.