OpenSSH keys have their own passwords. On my system there are a few things that are stored within login keyring: chromium safe storage for various electron based programs (Chromium itself, discord, vscode, unity hub), password or login token for Element (matrix client), svn password, login credentials for VM which was created using Gnome Boxes. All of which might be a software that you don't use or use in different configuration.
But since I don't have a fingerprint reader i can't verify that those things wouldn't work when logging in without password.
Edit: as a test I deleted the secrets stored by discord and Element, after restarting the programs both of them were able to login without reentering password. So while they are storing something within login keyring, it doesn't seem to be anything important, and actual credentials are stored elsewhere.