This is just Speculation but It sounds to me that Season Two is basically rebooting the first season of Batwoman. have there ever been shows where the entire show changes because the main character's Actor/Actress left after season one? I'm down with a Black Batwoman
I guess it's half a reboot. Like, it's still the same world and all the other characters will be the same, and Kate Kane still existed in that world, so in terms of story it's meant to be totally in continuity with the previous series. It'll certainly have some reboot-like aspects, though, since we are going to have to be introduced to this new character.
In terms of comparisons to other shows....that's a bit tricky. Most shows where main actors left had been going for a few seasons already, or were just cancelled. Out of the remaining few, most chose to recast rather than create a new character to take on the same role.
So none of these examples are perfect fits for what's happening with Batwoman, but some shows that had major characters leave early on, and kept going:
Stargate SG-1 - the TV series didn't go through any major cast changes, but two of the lead characters are from the Stargate movie, where they are played by Kurt Russell and James Spader. For television, the same characters were played by Richard Dean Anderson and Michael Shanks.
Doctor Who - with the original actor who was cast as the Doctor becoming less healthy and more difficult to work with after several years, the show's script editor came up with the idea that the Doctor, being an alien, could be given the alien ability to regenerate upon death, allowing for a new actor to take over the lead role, as the same character, but also with their own individual characteristics. This means that the lead actor can change whenever necessary. Though this didn't happen in the first season of the original production run (which didn't really have "seasons" as such), it did happen for the first season of the revival of Doctor Who, as Christopher Eccleston left after just one year.
Legends of Tomorrow - didn't really have any one "main" character as such, but mentioning this partly because it is an Arrowverse show and partly because it did go through significant cast changes after season 1. The Hawks were mercifully Poochied, the actor who probably got the most screen time (Wentworth Miller) left, and the actor playing the character who was the nominal leader of the team (Arthur Darville) had a significantly reduced role in season 2. There's a pretty stark dividing line between LoT season 1 and all the other seasons, and a lot of that is due to the cast changes.