CLN: remove _vendored/typing_extensions
- [x] closes #37119
- [ ] tests added / passed
- [ ] passes `black pandas`
- [ ] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [ ] whatsnew entry

As discussed in #37119, the vendored version does not serve its intended purpose.  Moreover, #37137 shows a way to get by without it.