CLN: remove check_series_type
Trying to clean up assert_series_equal and avoid usage of _internal_get_values; I'm finding that these functions are _weird_, and in particular categorical dtype handling is opaque
this is technically an api change, but not worth leaving it around, but can you add a note in the whatsnew `assert_series_equal` is a public function, so we should not just remove keyword arguments, I think.

(this broke geopandas CI) And for subclasses, this keyword can actually be useful. What was the reason you wanted to remove it? > What was the reason you wanted to remove it?

I'm trying to get rid of the `_internal_get_values` usages in `assert_series_equal` and finding the possible parameter combinations make that difficult.  Since this one was unused internally, it seemed like a good candidate.  If you want to re-introduce it, I have no objection. How is `_internal_get_values` and `assert_series_equal` related? That is only about checking the class type, but it's not related to the dtype? > How is _internal_get_values and assert_series_equal related?

_internal_get_values is called a couple of times in assert_series_equal (more before this PR).  Replacing the _internal_get_values usages with e.g. _values is the goal, but it turns out that breaks sometimes when we have Categorical _values.  assert_series_equal has several parameters that change the behavior when we have categorical, and I was trying to narrow those down (see also #32527) Sorry, that still doesn't explain to me the relation to `check_series_type`, which basically only is this part of the diff:

```patch
-    if check_series_type:
-        # ToDo: There are some tests using rhs is sparse
-        # lhs is dense. Should use assert_class_equal in future
-        assert isinstance(left, type(right))
-        # assert_class_equal(left, right, obj=obj)
+    # TODO: There are some tests using rhs is sparse
+    # lhs is dense. Should use assert_class_equal in future
+    assert isinstance(left, type(right))
+    # assert_class_equal(left, right, obj=obj)
```

so how is that related to (or required by) the `_internal_get_values` changes?

 > that still doesn't explain to me the relation to check_series_type

It isnt related, check_series_type was an innocent bystander that happens to be unused internally.  Again, I have no objection if you want to restore it. Well, having that the title of the PR didn't give the impression of being an innocent bystander .. ;) (also your "I'm trying to get rid of the `_internal_get_values` usages in assert_series_equal and finding the possible parameter combinations make that difficult." seemed to indicate this was related, hence my confusion).