Hello!
I'm having the exact same problem as you are at this very moment, and it has been about 45 minutes. I'm going to wait a bit and see if this changes.
To your questions:
The "pending owner verification" I think essentially means that records are propagating/verifications are pending and you don't have to do anything, although that is worded poorly imho. I never got any kind of e-mail confirmation either.
I used the Nameserver Connect method as well, and yes that's correct, it doesn't using the random-string verify records because you're using Squarespace's own nameservers in that case.
I'll report back here a bit later today with an update.