[3.15] gh-149504: Fix re-entrancy bug when .pth/.start file invokes site.add sitedir() (#149659) (#149799)

* 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

(cherry picked from commit b162307)

* Add myself back to CODEOWNERS

Author: warsaw

.github/CODEOWNERS

@@ -573,9 +573,9 @@ Lib/shutil.py                 @giampaolo
 Lib/test/test_shutil.py       @giampaolo
 
 # Site
-Lib/site.py                   @FFY00
-Lib/test/test_site.py         @FFY00
-Doc/library/site.rst          @FFY00
+Lib/site.py                   @FFY00 @warsaw
+Lib/test/test_site.py         @FFY00 @warsaw
+Doc/library/site.rst          @FFY00 @warsaw
 
 # string.templatelib
 Doc/library/string.templatelib.rst        @lysnikolaou @AA-Turner