There's IIRC 3 or 4 people in their department, they administer the whole building (wifi, security cams, LDAP, etc.), not only the on-premises servers. From what I gathered, our internal systems usually go down due to lack of disk space or some bug in the software which requires merely a reboot, it's not rocket science. Another thing is that our IT department (for internal systems) and the SRE department (for client-facing systems) have 24/7 on-call duty so it's unlikely that no one will respond.

The same thing that the cloud company would do. If there are other people there who share that guy's responsibilities, have them do it. If there aren't, you should have an on-call.

Cloud just outsources that problem to another business. Sure, they have better reasons to actually cover those positions and make sure they have on-calls and backup and a disaster plan, but just because you pay extra money for it doesn't actually make it work better if the company underlying it sucks.

What do you do if your cloud provider is down for 3 weeks?