For some reasons and governance rules an absence management must be possible.
Therefore I suggest that the Process Mining Admin can add the functional right to a second user. I also suggest to add this as a self service option to minimize/reduce manual effort by the cloud team.
After a follow-up, this ideas is explicitly about the Process Mining Admin as it is the only user who receives administrative mails etc.. There should be a way to add/change a substitute directly in the tool.
You can simply add data set and user admin rights to a user that grant them the same rights as the process mining admin user.