Added an edge case handler and a test case for Series.first("#M")
- [x] closes #51285
- [x] [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
- [x] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [x] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints) to new arguments/methods/functions.
- [x] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

As described in the above issue, first("1M") does not include timestamps of the last day of a month that are beyond "00:00:00". The problem happens to "2M", "3M", etc., where MonthEnd is being used.

To fix it, I added an if-statement in first() to check whether the offset variable is an instance of MonthEnd. If it is, the end date will be adjusted one day forward, and the returned range will end till the last timestamp before the end date.

I also added a test case in test_first_and_last.py and passed it.
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.