BUG: Special-case setting nan into integer series
~totally wrong, please ignore, will update~

~have updated, maybe it's not totally wrong anymore, but I'm off to bed now~🛏️ 

have woken up, and I think this is alright, so ready for reviews

Should integer interval dtype also not warn when setting `np.nan`? I've left that one out for now, but interval dtype is far less used than integer so I wouldn't consider that part a blocker to 2.1

Closes #54660
@MarcoGorelli - looks like you recently updated the title of this PR which seems to be causing other PRs to fail doc builds with:

```
Traceback (most recent call last):
  File "/home/runner/work/pandas/pandas/web/pandas_web.py", line 475, in <module>
    sys.exit(main(args.source_path, args.target_path))
  File "/home/runner/work/pandas/pandas/web/pandas_web.py", line 427, in main
    context = get_context(config_fname, target_path=target_path)
  File "/home/runner/work/pandas/pandas/web/pandas_web.py", line 382, in get_context
    context = preprocessor(context)
  File "/home/runner/work/pandas/pandas/web/pandas_web.py", line 334, in roadmap_pdeps
    for pdep in sorted(pdeps["items"], key=sort_pdep)
  File "/home/runner/work/pandas/pandas/web/pandas_web.py", line 328, in sort_pdep
    raise ValueError(msg)
ValueError: Could not find PDEP number in 'PDEP: Special-case setting nan into integer series (pdep6)'. Please make sure to
                write the title as: 'PDEP-num: PDEP: Special-case setting nan into integer series (pdep6)'.
``` Seems like it doesn’t even allow the “(pdep6)” at the end of the title I think it's just the label - I've removed that > Should integer interval dtype also not warn when setting `np.nan`? I've left that one out for now, but interval dtype is far less used than integer so I wouldn't consider that part a blocker to 2.1

Agreed this is not a blocker and can be done later. And I personally also have no strong opinion. I suppose if we follow the same logic, it also shouldn't warn?  thanks - merging then, have opened https://github.com/pandas-dev/pandas/issues/54790 regarding the interval case