[backport 2.3.x] API (string dtype): implement hierarchy (NA > NaN, p… #45376

Job	Run time
Test Conda Forge Recipe - Python 3.11	3m 3s
Test Conda Forge Recipe - Python 3.10	3m 11s
Install Extras - pyarrow	4m 8s
Install Extras - feather	4m 7s
Install Extras - output-formatting	4m 3s
Install Extras - hdf5	4m 13s
Install Extras - test	3m 58s
Install Extras - performance	4m 8s
Install Extras - clipboard	4m 6s
Install Extras - compression	3m 59s
Install Extras - xml	3m 58s
Install Extras - spss	4m 8s
Install Extras - plot	4m 6s
Install Extras - parquet	4m 8s
Install Extras - fss	4m 15s
Install Extras - all	4m 38s
Install Extras - gcp	4m 8s
Install Extras - aws	4m 13s
Install Extras - postgresql	4m 3s
Install Extras - excel	4m 1s
Install Extras - consortium-standard	3m 55s
Install Extras - mysql	4m 2s
Install Extras - computation	4m 12s
Install Extras - sql-other	4m 0s
Install Extras - html	4m 5s
	1h 40m 48s

Provide feedback