BUG: Don't clean docs and open browser in code_checks
- [ ] closes #xxxx (Replace xxxx with the GitHub issue number)
- [ ] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [ ] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [ ] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints) to new arguments/methods/functions.
- [ ] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

Ref: https://github.com/pandas-dev/pandas/pull/46806#issuecomment-1152922326

In regards to not cleaning the docs at the end, when I'm wrapping up a PR, I'm typically building documentation and running code_checks. Right now these are at odds with each other since the docs are cleared in code_checks. Can remove if there is opposition to this change.
Nice! I think this is a nice cleanup. Thanks @rhshadrach 