Joker is it's own thing
I disagree, I find it hard to believe that characters like Superman and Weasel are from the same universe
if Gunn directed MoS, he'd be like idk... Silver Age Supes or some shit, something out of Superfriends and if Weasel was a character from Snyder movies, he'd be like some grimy creepy monster thing, all edgy and shit.
My point is that MoS, BvS, WW, Suicide Squad 2k16 and the Snyder Cut all feel like the same universe, same visual style, same level of grimyness/edgyness and (more or less subjective) realism
With movies like Suicide Squad 2k21, Aquaman and Wonder Woman 1984 my suspension of disbelief gets annihilated with both of them, either via comic booky goofiness (TSS, Aquaman) that wasn't present in any of the previous movies, or via explicit character assassinations and huge retcons/continuity errors (WW84). With all of them you can see that the director was given cart blanche and so they didn't give a fuck about trying to align with the previously established tone and just did their own thing. The result is that SS 2k21, Aquaman and WW84 stick out like sore thumbs from the other movies.
Somehow I don't have this problem with Shazam despite the lighter tone, I can absolutely see it as part of the Snyderverse/DCEU despite the highjinx.
And I don't want to talk about Birds of Prey.