Ohio is just used as a replacement for weird or cringey. That's really it. Ohio rizz is what they call it when someone is awkward, weird, or creepy when flirting.
You ask the important questions. That is a tough one. I imagine that to most gen alpha kids, an adult using their slang would be considered Ohio behavior, but it probably depends on how Sigma they consider the teacher to be.
I'd assume middle school teachers are fairly cringe just for being middle school teachers but if one is trying to learn the new lingo, at least they're trying to communicate.
Then again, I was a Trekkie misfit in the 70s and 80s when we didn't have TNG yet, and was commonly regarded as skibidi ohio.
Also, to be fair, Ohio was cringe and weird in the 1960s, especially after Kent State and CSN made Ohio into a folk song, and it's lit if that's where Alpha vibe gets its cred.