gh-149504: Fix re-entrancy bug when .pth/.start file invokes site.addsitedir() (#149659)

* Add re-entrant tests for gh-149504
* Add end-to-end integration test coverage

This ensures that future whitebox internal test changes do not regress the
public surface semantics.

* Implement a state class to process .pth and .start files

By using this state class and managing implicit and explicit batching, we make it structurally
impossible to get bitten by re-entrant site startup processing.

Fixes #149504