I use a private cloud — can Relay still sync my to-dos?

Quite possibly — but read the caveat at the end. Relay reads your to-dos from Supernote's official Cloud, and Supernote doesn't sync to-dos to private clouds at this time. So if you signed out of your Supernote account when you set up your private cloud, your to-dos aren't syncing anywhere — and Relay has nothing to work with.

The good news: on the device, those are two separate settings. Settings → Drive is where your notes and files sync — that's what private cloud takes over. Settings → My account is your Supernote sign-in, and it's what syncs your to-dos. Private cloud doesn't touch it. So even with all your notes and files going to your private cloud, you can sign back in to My account with your Supernote login and turn on to-do syncing — and only your to-dos will sync through the official Supernote cloud. That's all Relay needs.

The honest caveat: I don't run a private cloud myself, so I haven't verified this end-to-end. If you're on a private cloud, treat the free trial as your test bench — every feature works, no card needed — and see for yourself before buying. And whichever way it goes, I'd genuinely appreciate hearing the result through the contact form: you'd be settling it for every private-cloud user who comes after you.