OK, I thought there was something wrong with the Omni Sync Service, when you send email to create tasks. I checked my email server mail log, and saw that the emails were in fact being accepted (Omni email server replied correctly).
When I went back to my iPad, a box popped up asking for my sync username and password. After I put it in, about 20 tasks came flying in!
So when I restored my new iPad Pro from an iCloud backup, apparently it didn’t copy over my authentication to OmniFocus.
I just don’t know why it didn’t prompt me before - I’ve used it several times and it didn’t seem like it was syncing, but I deferred looking into it.