BUG: Remove np._get_promotion_state usage
- [x] closes #59817 
- [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).

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 2.2.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 081dcdee8d754af90e307cf2311b06b3d02fae2a
```

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

```
git commit -am 'Backport PR #59818: BUG: Remove np._get_promotion_state usage'
```

4. Push to a named branch:

```
git push YOURFORK 2.2.x:auto-backport-of-pr-59818-on-2.2.x
```

5. Create a PR against branch 2.2.x, I would have named this PR:

> "Backport PR #59818 on branch 2.2.x (BUG: Remove np._get_promotion_state usage)"

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).
                