Which cloud service does this?

I have no idea. I know Azure does for the student/msdn/and similar accounts which are the only cloud services I use for personal projects. So I Azure doesn’t even have my credit card.

Cloud Run lets you cap the number of instances when you create a service. So you can just set max_instances to 1 and you never have to worry about a spambot or hug of death from blowing up your budget. I run all my personal sites like this and pay (generally) nothing.