DEPR: by_row="compat" in DataFrame.apply and Series.apply
- [ ] closes #xxxx (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.

Followup to #53400. Fell off my radar that this needed to be deprecated. Will only be able to specify `by_row=False` in 3.0, and then the argument will be removed in 4.0.

cc @topper-123 
:facepalm: I forgot there is opposition with enforcing this deprecation in #52140.