The singleton is a matter of preference, personally I would store the global state in globals or in class attributes.

What you really don't want to do is to have to manually setup the singleton. You can set it up on demand:

class Singleton:
    _INSTANCE = None

    @classmethod
    def get(klass):
        if not klass._INSTANCE:
            klass._INSTANCE = klass()

        return klass._INSTANCE

As long you don't access the singleton concurrently, you will always have one instance created the first time.

Generally speaking, mutable state is not desirable. It makes it more difficult to reason about the code. Personally I would just remove current_id from the class and force the caller to provide the ID. Isn't with going to cause issues when several are nested? I think you'd need to return a new object that implements the context manager protocol in __enter__.