It doesn’t support global state. Instead you’d write a “process” that’d respond to requests with the state at time of request. Another request could mutate the state, but each request is processed one at a time. So a “bucket” type data store (object store etc) would likely be implemented as “server” that returns the state. If the objects were large you could pass a URL/handle to the file which you’d retrieve later.
These processes/servers/whatever are running inside the language VM and are SUPER lightweight. Multiple language VMs can be tied together so the actual processes can be distributed across a fleet of physical hosts in a data center - this would be transparent to how you write the code.
If you wanted to implement that in native AWS primitives you’d probably run a lambda function to transform an http request into a S3 bucket address, then you’d go and make an s3 request to download/modify the file. Or the lambda would make some modifications to the file.
So, that’s the prior art on a hypothetical distributed language handling global state, which fwiw is basically how “cloud” systems work today.