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Has there ever been a female world chess champion (or, before the title existed, any woman who was widely regarded as the best chess player in the community or region)?

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Yes there is a female world chess champion. Currently that person is Ju Wenjun, who won the most recent Women's World Chess Championship against Aleksandra Goryachkina.

If you're asking whether there has been a female open-category world chess champion, the answer is "no", in fact no woman has ever beaten a reigning undisputed world chess champion at classical time controls. The woman who came closest was Judit Polgar, considered the strongest female chess player of all time. She is the only woman to have played in an exclusive world chess championship*, the 2005 edition, where she finished last.

As for whether she was ever the best player in her region, that is debatable - although she was ranked as highly as 8th in the world, at the time she had a countryman Peter Leko who was also in the world elite. I did not check every rating list, but in the July 2005 list (which is when Polgar hit her highest rating), Leko was still rated some 30 elo above her.

*Prior to the 1990s, world championships were always decided in a one-on-one match where the champion played against a challenger who had won the "candidates tournament". During the 1990s there was some turmoil in the chess world such that there were multiple world champions and the title was disputed. FIDE, the organizing body behind chess, experimented with different formats for the world championship. In some years they had big 100+ player knockout tournaments, and in 2005 they had a much more exclusive all-play-all double round robin. Judit Polgar is the only woman to have played in such an exclusive (and thereby more prestigious) tournament.

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    Solely based on the fact that there exists a women's championship (thus precluding male competitors) but no men's championship - only an open championship where gender plays no part in qualifying for the event, strongly suggests that the strongest playing women, for whatever reason, are not as strong as the strongest playing men.
    – Bohemian
    Jul 23, 2020 at 6:25
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    @Bohemian that's well-established, there are usually no more than 1-2 women in the top 100 rating lists. The current open-category world champion, Magnus Carlsen, is rated ~250 elo above Ju Wenjun (although notably the world's strongest woman is Hou Yifan, who is not very active right now and like Polgar refused to participate in recent women's world chess championships; Carlsen is only ~200 elo above Yifan).
    – Allure
    Jul 23, 2020 at 6:47
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There's a correct list of World Champions (preceded by a list of players regarded as the world's strongest before the title existed) on Wikipedia. All of them are men, there hasn't been any woman considered to be the strongest chess player at a certain point of time.

As for regional championships, Judit Polgar, mentioned by @BenjaminCosman, won the Hungarian National Championships. There are probably others who achieved this.

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There has not yet been a female world champion in chess. According to Wikipedia, Judit Polgár is "generally considered the strongest female chess player of all time"; see the article for her many accomplishments.

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Well, there is a regional (and pretty famous) female chess player I have heard of. Her name is Koneru Humpy. Her Elo rating is 2606 according to Wikipedia.

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    Humpy is not nearly the best Indian chess player though - she's outrated by former world champion Anand and her countrymen Pentala Harakrishna, Santosh Vidit, and B. Adhiban.
    – Allure
    Jul 21, 2020 at 8:27

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