I was aware of the login UID for auditd logging as a difference but as you say, that is only really helpful if the logs are shipped somewhere else or tampering with them is otherwise prevented for admin users. It is not quite the same but the auth.log entries sshd produces on login also contain the key fingerprint used to login these days so on a more limited scale you can at least tell who logged in when from those (or whose key but that is no different than whose account for the sudo approach).
you should consider doing it right from the start.
Do you have any advice on how to use the sudo approach without having a huge slow down in every automated process that requires ssh user@host calls for manual password entry? I am aware of Ansible but I am honestly very sceptical of Python tools since they tend to break easily and often from my past experiences and I would like to avoid using additional ones for critical tasks. Plus Ansible in particular seemed to be very late with their Python 3 transition, as I recall I uninstalled it when it was one of the last tools left that did not work with Python 3.