TST: fix tests for mixed int string index
- [x] closes #54072
Added in conftest's `indices_dict` an entry:
```
"mixed-int-string": Index([0, "a", 1, "b", 2, "c"])
```
Adding "mixed-int-string" causes some tests to fail, fixed these tests.

@jbrockmendel, I corrected my PR, could you please take a look at the update? This pull request is stale because it has been open for thirty days with no activity. Please [update](https://pandas.pydata.org/pandas-docs/stable/development/contributing.html#updating-your-pull-request) and respond to this comment if you're still interested in working on this. > This pull request is stale because it has been open for thirty days with no activity. Please [update](https://pandas.pydata.org/pandas-docs/stable/development/contributing.html#updating-your-pull-request) and respond to this comment if you're still interested in working on this.

Yes, this PR is still actual. @jbrockmendel, I updated my PR, could you please take a look at the update? I added an entry: `"mixed-int-string"` in conftest's `indices_dict` and corrected tests, ci - green. @MarcoGorelli could you please take a look at this PR? gentle ping @jbrockmendel  Looks like this PR has gone stale and has conflicts now. Closing to clear the queue but if interested in contributing please resolve the conflicts and we can reopen