Move publish_active to avoid race condition

[strawgate]

Tests pass, appears to be publishing documents

[strawgate]

Fixes https://github.com/legrego/homeassistant-elasticsearch/issues/301

[github-actions[bot]]

Coverage Report

File	Stmts	Miss	Cover	Missing
__init__.py	0	0	100%
elasticsearch
__init__.py	90	2	97%	208–209
config_flow.py	252	28	88%	85, 124, 232, 314, 337, 351, 392–395, 397–398, 400, 402–404, 406–407, 421–422, 426, 466, 472, 512, 587, 596, 630–631
const.py	33	0	100%
entity_details.py	33	0	100%
errors.py	28	3	89%	51, 60, 67
es_doc_creator.py	183	0	100%
es_doc_publisher.py	260	15	94%	103, 245–246, 262–263, 366, 466–467, 469–470, 472–476
es_gateway.py	100	19	81%	82–83, 102, 118–120, 122, 124–125, 127–131, 133–137
es_index_manager.py	123	8	93%	243–244, 261–262, 267–268, 297–298
es_integration.py	37	2	94%	43–44
es_privilege_check.py	55	0	100%
es_serializer.py	10	1	90%	17
es_version.py	30	0	100%
logger.py	2	0	100%
system_info.py	25	1	96%	37
utils.py	4	0	100%
TOTAL	1265	79	93%

Tests	Skipped	Failures	Errors	Time
95	0 :zzz:	0 :x:	0 :fire:	7.403s :stopwatch:

[strawgate]

@legrego I'm not actually sure how to hotfix 0.7

We probably don't want to release main, do we make a 0.7 branch from the 0.7 tag, merge this PR into that, and then cut a new release?

If so can you make a branch I can backport into?

If not please advice or feel free to steal this change and do it the right way