Kate Mulgrew got the honor of becoming the first female captain to lead a Star Trek series with the debut of Voyager in the 1990s. The flagship show for the UPN network, Voyager was the first series that Trek has ever done that centered on a woman as the captain of a starship and in turn, many of the advertisements billed her as the first female captain.
That's not true. But it also is. The context about the first ever is fair in the fact that Mulgrew was in fact the first female lead to take over a titular ship as captain. No woman in the history of the franchise can say she predates Mulgrew, and she opened the door for the likes of Sonequa Martin-Green and others to take that seat after her.
Yet, if we're looking at the timeline of events, Screenrant is right in saying the "first" female captain is actually from the Star Trek: Enterprise era of shows. Portrayed by Ada Maris, Captain Hernandez from the Enterprise episode "Home" and beyond, she becomes the first woman to canonically be a captain in the Star Trek universe.
Yet, if we're looking at who played the first female captain in all of Star Trek's history, that would go to Madge Sinclair, who played the captain of the USS Saratoga in the film Star Trek IV: The Voyage Home. While never given a name, Sinclair is the first woman to ever appear in a Star Trek property with the given rank of captain.
Sinclair would also go on to play the mother of Geordi La Forge in Star Trek: The Next Generation, as Silva. Silva La Forge was also a captain, much like Sinclair's prior appearance in the franchise. Thus making Sinclair the first actress to appear as a captain twice across two different iterations of the franchise.