TST: reintroduce check_series_type in assert_series_equal
- [x] passes `black pandas`
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`

Re-introduced `check_series_type` in `assert_series_equal` which was recently removed in #32513. It was a part of public API which is not used internally, but it is used elsewhere (like geopandas). Discussion in #32513 suggests that it should be put back where it was.
I think worth completely reverting rather than part of the original PR

@jbrockmendel @jorisvandenbossche  > I think worth completely reverting rather than part of the original PR

Why is that?  #32513 included some non-downstreaming-breaking improvements Yes, just adding back only this is perfect IMO. The rest of the PR was actually completely unrelated to this change (regardless of the title of the PR that seemed to indicate otherwise). We might want to add a test though Added a test @simonjayhawkins this is passing now. Are you OK with including the fix here?

cc @jbrockmendel  > lgtm. maybe #32670 (comment)

Ah, yes, forgot that. That actually simplified it a lot lgtm