At least for me this analysis seems to be correct. I have not unlocked the bootloader and I have not installed a custom ROM and the update to Android 13 (C.073) went fine. I have an uptime of >25 hours and not a single reboot or any other issue that might be related to the Android system update. On the contrary, my FP4 feels better (more responsive) since the update and even the overly aggressive vibration seems to have improved.
I did, however, modify some system settings including developer options (enabled USB debugging and a few other settings) and I did disable/uninstall a few core apps (e.g. GBoard, the Google app, YouTube, …) using universal android debloater as described in this thread (with a few deviations).