Update `to_gbq` wrapper method to contain `api_method` parameter
ENH: add api_method parameter and some documentation
DOC: update dependencies to require at least version 0.16.0 of pandas-gbq

- [ ] closes #46117
- [ ] [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.

looks fine. @tswast ok here? Yeah appears that pandas-gbq requires pyarrow>=3.0 while pandas still supports pyarrow>=1.0.1. To support this for 1.5 we would need to do the kwargs trick mentioned https://github.com/pandas-dev/pandas/pull/47539#pullrequestreview-103004336 This pull request is stale because it has been open for thirty days with no activity. Please [update](https://pandas.pydata.org/pandas-docs/stable/development/contributing.html#updating-your-pull-request) and respond to this comment if you're still interested in working on this. Thanks for the pull request, but it appears to have gone stale. If interested in continuing, please merge in the main branch, address any review comments and/or failing tests, and we can reopen.