Must be different types of Non-O. I'm on a Non-O volunteer (with work permit; visa originally established abroad) and have never had to show bank statements.
Probably only the consulate could you tell absolutely, but I would think not.
I came in on Test & Go (though applied under CoE) with a re-entry permit (non-O). The passport control agent basically asked if I wanted to use that or do a tourist visa (since my non-O was expiring soon). I stuck with the re-entry since I knew I'd be renewing soon, but he didn't care about what the pass was granted under.
Traveling together can use 1 room. There's no reason to keep separate as if 1 of you tests positive, my understanding is all of you go on quarantine protocol.
With "Exemption from Quarantine (aka Test & Go)", it's 1 night OR negative result. You should be free to venture out now. Sadly, it sounds like the hotel doesn't have accurate information, but maybe their own process it different with their certificate.
If you already have your Thailand Plus certificate based on the SHA+, you should be good. Phuket tests at the airport anyway, so the only thing the hotel should do is pick you up and give you an ATK test kit to take with you after leaving.