ENH: Bring `assert_equals` into the public API

[rhshadrach]

assert_equal was added in #22033 after other testing methods were exposed in the public API in #16003, and I haven't been able to find any discussion on whether this should be added. I recently ran into a case where it could have been useful.

If we are to go this route, then I think two enhancements should be made first:

• Improve the docstring
• Raise if the objects passed are not pandas objects (Series, DataFrame, EA, Index, etc).

For the 2nd, the current implementation has a specific check for strings and a fallthrough for all other objects. These two cases are hit by 9 tests that would need to be changed.