Screenrant answered it pretty well:
Earth 89: Tim Burton's Batman Movies
Tim Burton's Batman films are represented in one quick cameo, which confirmed it as Earth-89. Danny Elfman's familiar Batman theme plays as the Bat-Signal burns bright in the red skies over Gotham City. This is observed by a man in a trench-coat and fedora, who mutters "I hope you'...
I believe the quote you are referencing is:
"Tell us a story," said the March Hare.
"Yes, please do," pled Alice, and so the Dormouse began "Once upon a time, there were 3 little sisters.
That being the case, Alice/Beth is Kate's sister but Mary Hamilton (played by Nicole Kang) is their step-sister being the daughter of Jacob Kane'...
After Batwoman S01E04 and before S01E05.
From Caroline Dries's tweet
After 104 we are officially caught up to Elseworlds! #batwoman
Later Russ Burlingame continued:
Because the writers wanted to show Kate's origin story, they had to go back to before she was Batwoman, which required some catching-up in the first few episodes. Instead of it being a week ...
From Crisis: Episode 2 (Batwoman)
Legends of Tomorrow have retired and Mick Rory is left inhabiting the Waverider
Batman (Kevin Conroy) has retired and can only move thanks to an exoskeleton.
Superman of this Earth is killed by Lex Luthor wielding the Book of Destiny
Superman (Tom Welling) has given up his powers and ...
So I want to know how much should I know from Arrowverse before jumping into Batwoman?
At present (Oct 2019), Batwoman has no crossover or involvement with the rest of the Arrowverse that you need to catch up on although watching the original "pilot" which was the "Elseworlds" crossover episodes in December 2018 which introduced that character might be ...
Brad Hunter (Comics - appears in 1 issue)
Lacy Warfield (Donnerverse - Superman IV: The Quest for Peace
Mark Spencer (Comics - appears in 6 issues)
Jeff Hage (Comics - 9 issues)
Jennifer Owens (Comics - 13 issues)
Franklin Stern (Comics - 33 issues)