Since it was originally spun off from Supergirl, I tend to still consider it Arrowverse, just on another Earth.
Yes, S&L is explicitly part of the Arrow/CW multiverse, since John Henry & Natalie Irons's Earth was destroyed by the antimatter wave in the Crisis.
I'd bet that it was originally intended to be on the same Earth as the other series--and that got changed, probably because the show runners knew the clock was ticking on the end of the other series.
We know for a fact that it
was initially meant to be set on Earth Prime; the producers have said that they only made the decision to retcon it into a separate Earth during season 2, which is why season 1 featured a John Diggle appearance that alluded to his ongoing Green Lantern-tease arc in his guest appearances on other shows that year. It wasn't until the season 2 finale that it was made explicit to the audience, through dialogue establishing that Superman was the only superhero on his Earth.
Before then, it was only implied by the lack of any mention of Supergirl/Kara or any other Arrowverse heroes. The producers in season 1 were open to a Supergirl mention or appearance, but every time they thought about including one, they decided it would just be a distraction from their own story. And after more than a year of effectively ignoring the other shows (except in the Diggle episode), they finally began to realize they should just make a clean break and let the show be in its own independent continuity.
I'm not sure there's much point in splitting multiversal hairs when considering the CWDC series in general, especially after "Crisis" made them all explicitly part of a larger whole. Are Stargirl or Gotham Knights somehow fundamentally distinct from the other shows? Not from where I'm sitting.
Of course they are, since they're set in separate continuities with separate interpretations of their shared characters and concepts. Yes,
Crisis on Infinite Earths established in passing that
Stargirl was the new "Earth-2" in the Arrow multiverse, but there was never an actual crossover between its characters and the Arrowverse characters, unless you want to believe its version of Jay Garrick was somehow the same one from Earth-3 during his multiversal travels. The only other show that had a direct crossover with
Stargirl was
Titans, which isn't in the Arrowverse (except in the sense that all DC live-action continuities are implicitly in the same multiverse now). And
Gotham Knights may have been from the same production company as the Arrowverse shows, but it was a completely self-contained show, not lasting long enough for any kind of multiversal shenanigans.
A fictional multiverse is not something that has an actual existence transcending the series themselves. It's merely a storytelling conceit within certain stories. If the stories themselves contain no mention of alternate universes, then they aren't "part" of any multiverse, they're just self-contained stories, the same as most stories.
