Yeah, all the inconsistencies and continuity missteps in regards to Carter/Katar and Sharon/Shiera/Kendra have been exhaustively explained and re-explained. There's no need to belabor it any further.
The struggles of the various Hawkman/Hawkgirl titles from the past several decades have had weren't about readers being confused with continuity, it's that the characters are too niche to support an ongoing series. Not every superhero needs to have an ongoing. Some are better suited to guest appearances, team books, and mini-series.
I still think they should have just made Kendra Shayera's daughter.
So is the current status that the reincarnations go across time and space?
So currently Hawkman is Carter Hall is Katar Hol, reincarnated in the Thanagar body?
Hawkwoman is Shiera is Shayera, reincarnated in the Thanagar body?
Hawkgirl is Kendra Saunders, niece of Shiera. Human body (possibly once housed the reincarnation but no longer).
Is this all true?
I think Kendra is still supposed to be a reincarnated Shiera as well.
But it would be much better for her to simply be Shiera's legacy and free from the whole reincarnations angle. Having both Shiera and Kendra around at the same time as reincarnations of the same spirit is too confusing and adds nothing to the stories.
The Hawkworld mini and the Hawkworld series that followed Is my personal favourite of all the Hawkman runs I’ve read...there was no “baggage” at all till action moved to Earth and John O started worrying about continuity fixes for some obscure reason.
In general Hawkman continuity has got so involved that I just wish each run just gave a brief outline of how it regarded origin of the Hawkman/woman used in that series and then forgot what happened in previous series.