I closed the game fully, that wasn't the issue. It was NEVER open during the short time the date on my Switch had changed.
The only issue I can think of is maybe I should have set the clock, not to midnight, but after 5 AM... which I think is when villagers usually move out/in. But I didn't think it'd matter if it passed 5 AM on the exact same date it was set to?
Anyway, consider this a cautionary tale, people

Sorry for my mini-rant- I want just totally stunned and frustrated! Hopefully I can make the best of it and find Ankha a home- I may dislike her, but I know some people spend tons of NMTs just to find her (which somehow made me feel more annoyed to get her, lol)