gh-120161: Clean Up the Managed Static Types State

[ericsnowcurrently]

In gh-120182, the approach I took aimed to fix the problem with minimal churn, for the sake of backporting. This change builds on that with what I consider the cleaner approach I would have taken.

The key changes are:

• move more data into the global runtime state
• at the interpreter level, consolidate the builtins and extensions state
• add many more asserts to ensure consistency

• Issue: Objects/typeobject.c:143: managed_static_type_index_get: Assertion managed_static_type_index_is_set(self)' failed.` in 3.13.0b2+, with freezegun #120161