BUG: Period constructor raises instead of ignoring when passing a string with extra precision(pico, femto, etc.)
- [ ] xref #50149 (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.

Honestly, it might be worth to kill ``parse_time_string`` entirely. It seems like it is only used for Period, and some DatetimeIndex str slicing logic.

@MarcoGorelli interested? I'll take a look, thanks for the ping! ping @jbrockmendel  thanks @lithomas1 