DOC: EX01 ({Categorical, Interval, Multi, Datetime, Timedelta}-Index)
- [x] Towards #37875.

Also removing some items from `ci/code_checks.sh` that have already had examples on the main branch.
Thank you for your PR @Charlie-XIAO!

Some of items that you removed from the file `ci/code_checks.sh` thinking that they already have examples, should not be removed. Many methods share one (the same) docstring and it _looks_ like that.

For example `pandas.CategoricalIndex.codes` seems on the dev website as it had an example already. But the example is actually for `pandas.Categorical.codes`.  

I only checked a couple of methods that were removed. It would be great if you could double check the rest please. Thanks a lot, your help is very much appreciated. :-)  
 @DeaMariaLeon Thanks for the reminder! I see what you mean, so those examples should be modified. Maybe I can just do them in this PR as well. I also need to run `scripts/validate_docstrings.py` since there is a decent number of errors.