BUG: fixes weekday for dates before 1752
- [x] closes #53738 (Replace xxxx with the GitHub issue number)
- [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 an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

Approach was to switch to implementing [Gauss's algorithm for weekday](http://berndt-schwerdtfeger.de/wp-content/uploads/pdf/cal.pdf).  Ended up being quite interesting.  nice work!

just got a couple of requests:

- on the unit test side, could you add a couple of negative dates please?
- could we also add a parametric test using hypothesis please, in which we compare the output against the standard library output? feel free to reach out if you're not sure how to do this Thanks @MarcoGorelli! 

Haven't used Hypothesis before by tried to follow the patterns elsewhere in the codebase. 
Also by "standard library" I assumed you were referring to `datetime`. Let me know if I missed the mark any what you were looking for.  yup, that's right! one way to do it could be to make a dict with
```python
{0: 'Mon', 1: 'Tue', ...}
```
and then generate a random datetime `datetime`, and compare `Timestamp(datetime).weekday` with `datetime.strftime('%a')`

something like that Sorry @MarcoGorelli did you see this push https://github.com/pandas-dev/pandas/pull/53795/commits/ca826d8b30838da53794e8b0c7108844c678d130 ? 

I had already added the Hypothesis driven test before my pervious note, sorry for the confusion.   CI failure is unrelated, but probably safer to wait til that's addressed before merging Owee, I'm MrMeeseeks, Look at me.

There seem to be a conflict, please backport manually. Here are approximate instructions:

1. Checkout backport branch and update it.

```
git checkout 2.0.x
git pull
```

2. Cherry pick the first parent branch of the this PR on top of the older branch:
```
git cherry-pick -x -m1 20530b1f45045bfb95b0a79cda70fa7b804c9a6a
```

3. You will likely have some merge/cherry-pick conflict here, fix them and commit:

```
git commit -am 'Backport PR #53795: BUG: fixes weekday for dates before 1752'
```

4. Push to a named branch:

```
git push YOURFORK 2.0.x:auto-backport-of-pr-53795-on-2.0.x
```

5. Create a PR against branch 2.0.x, I would have named this PR:

> "Backport PR #53795 on branch 2.0.x (BUG: fixes weekday for dates before 1752)"

And apply the correct labels and milestones.

Congratulations — you did some good work! Hopefully your backport PR will be tested by the continuous integration and merged soon!

Remember to remove the `Still Needs Manual Backport` label once the PR gets merged.

If these instructions are inaccurate, feel free to [suggest an improvement](https://github.com/MeeseeksBox/MeeseeksDev).
                