PERF: Speed up Period construction
- [ ] closes #38312 (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.

ASVs.
```
       before           after         ratio
     [1d5ce5b3]       [b47aa45a]
     <main>           <period-speedup>
-     8.18±0.06ms       5.50±0.1ms     0.67  period.PeriodIndexConstructor.time_from_ints_daily('D', False)
-     8.06±0.06ms       5.36±0.1ms     0.67  period.PeriodIndexConstructor.time_from_ints_daily('D', True)
-     8.94±0.08ms      5.31±0.04ms     0.59  period.PeriodIndexConstructor.time_from_ints('D', False)
-     8.77±0.09ms       5.20±0.1ms     0.59  period.PeriodIndexConstructor.time_from_ints('D', True)

SOME BENCHMARKS HAVE CHANGED SIGNIFICANTLY.
PERFORMANCE INCREASED.
```

parse_time_string already calls string_to_dts(parse_iso_8601_datetime), which I think is the only function that can currently parse nanoseconds(dateutil can't do it IIRC). 
are the improvements in parsing.pyx independent of the improvements in period.pyx? needs rebase, otherwise LGTM Thanks for the reviews.

This PR depends on  #50417, though, so need someone to review/re-review there. ping on green