Speaking of retcons, if Pennyworth and Gotham were somehow set on Earth-38, that headcanon would create an logical (plus historical and geographical) issue after Crisis - that being Berlin.
Pennyworth had an off-handed line in episode four about the German Reich (a fourth Reich?) allowing autonomy to the Netherlands in a committee in
Berlin.
Meanwhile on Earth-1, in the Legends of Tomorrow episode "No Country for Old Dads", East and West Berlin are a thing as well as East and West Germany.
If Earth-38 included Gotham and Pennyworth and that Earth merges with Earth-1 in Crisis...that would extremely alter the events of the aforementioned Legends of Tomorrow episode.
But that episode is integral to the storyline so...
the cold fusion scientist would be stuck in Germany regardless.
Just a thought. Felt like sharing.
EDIT: It's probably inevitable; Batwoman's Gotham City is (almost) EXACTLY like the one from the show Gotham.
As seen here:
2019 - 15 years = 2004 (i.e. the supposed year when Gotham's series finale took place?)