It's just a database service. You don't run the servers. You pay someone to do that and you just connect to it and use it and someone else maintains the servers, storage, scaling, backups, patches, etc., according to some SLA and other terms.
There are indeed servers somewhere. "Serverless" is misleading cloud speak for the otherwise easily understood concept of a service.
They almost never shut down the actual VMs, they are simply re-allocated. (Semi)Auto scaling exists behind the scenes but once a provider becomes popular enough the VMs become more expensive to stop.
It's just a database service. You don't run the servers. You pay someone to do that and you just connect to it and use it and someone else maintains the servers, storage, scaling, backups, patches, etc., according to some SLA and other terms.
There are indeed servers somewhere. "Serverless" is misleading cloud speak for the otherwise easily understood concept of a service.