For me it's not just Touch ID, but login/logout overall.
If I'm logged in and I lock my screen, the screen saver with the fly-by field is shown. If I then press any key, nothing happens for like 10-15 seconds (but I do here the "blip" sound of a key press when pressing any key) before the login prompt even appears. During this period, the beach ball also appears and disappears a couple of times.
If I then either use Touch ID or enter my password and press enter, it freezes for another ~10 seconds before logging in. Furthermore, even if I enter the wrong password, it freezes for 5+ seconds before any feedback (where the password field "bounces" to indicate wrong password). So it does not seem to be related to the login process as such being slow, but rather the process of showing the login screen AND the process of validating the credentials (be it password or touch ID).
Mac M1 Pro, Sonoma 10.6.1, managed through InTune MDM.