BUG: round on object columns no longer raises a TypeError
- [x] closes #61206 (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 [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.

`pre-commit.ci` is timing out and the 2 failed unit tests are canceled operations.  @KevsterAmp could you target this PR to `main`? We have a process to backport this PR to the `2.3.x` branch after it is merged to main Rebased to main and forced push the branch.

@mroeschke since we're targetting to main. Should I add to `whatsnew/v3.0.0.rst` and remove the current `whatsnew/v2.3.0.rst`? > Should I add to whatsnew/v3.0.0.rst and remove the current whatsnew/v2.3.0.rst

No need. It's implied that all fixes in 2.3 apply to 3.0 Thanks @KevsterAmp  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 2.3.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 6a2da7ad16cff82f0eadbec04e921baf6c0ae8fb
```

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

```
git commit -am 'Backport PR #61399: BUG: round on object columns no longer raises a TypeError'
```

4. Push to a named branch:

```
git push YOURFORK 2.3.x:auto-backport-of-pr-61399-on-2.3.x
```

5. Create a PR against branch 2.3.x, I would have named this PR:

> "Backport PR #61399 on branch 2.3.x (BUG: round on object columns no longer raises a TypeError)"

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).
                