General cleanup of test_pydoc (GH-29459)

- Uniform usage of `test.support.requires_docstrings` instead of a
  local check for `-OO`.
- Added `requires_docstrings` to a couple more methods that need it.
- Replaced a few instances of `test.test_pydoc` with `__name__` to allow
  for different methods of running just this test file.
- Rewrote `test_server` to run faster and better test the server.
- Removed unused import.
- Removed unused locals.
- Minor whitespace cleanups.