BUG: preserve timezone info when writing empty tz-aware series to HDF5 
- [x] closes #20594 (coupled with #37069 for empty tz-aware dataframes)
- [x] tests added / passed
- [x] passes `black pandas`
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [ ] whatsnew entry

xref #20595 (stale PR that looked into this)
> ok i am not sure how to grok this one as i think its on top of the other; in the future put them both in 1 PR is ok for this size change, or now, wait till the other is merged then rebase this one (or make this orthogonal)

Ok will do! For this one I'll wait until the other is merge (since this is a dependant) @jreback this is ready for re-review
- [x] rebased against master (includes  #37069)
- [x] rewrote the tests from here and  #37069 using `tz_aware_fixture`
- [x] added whatsnew CI Green + ready for re-review thanks @arw2019 