DEPR: object inference in to_stata

[jbrockmendel]

• [ ] closes #xxxx (Replace xxxx with the GitHub issue number)
• [ ] Tests added and passed if fixing a bug or adding a new feature
• [ ] All code checks passed.
• [ ] Added type annotations 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.

The "do X instead" won't actually work until 3.0, so this has to wait until then (and can't write the whatsnew until the 3.0 file exists). Putting this here so I don't forget about it.

[github-actions[bot]]

This pull request is stale because it has been open for thirty days with no activity. Please update and respond to this comment if you're still interested in working on this.

[mroeschke]

Now that we have the 3.0.0.rst file now, interested in following up?

[jbrockmendel]

Going to hold off until #55901 goes in

[jbrockmendel]

it looks like we don't have any test cases that get to the relevant path. editing test_big_dates to use expected.astype(object).to_stata fails pretty badly; it looks like in the delta=True case by storing microseconds instead of milliseconds.

two options: first is to change the relevant path to call infer_objects() and then recurse, second is to just rip out the now-identified-as-buggy path. preferences?

[bashtage]

Probably just take it out. Simplicity is its own reward.