Does SimpleX even sync messages between the phone and the desktop? Last time I checked they didn't unless you were maybe on the same network
Depends on what you mean by sync. It has limited support for tethering a mobile device to a computer on the same LAN, but lacks the kind of independent multi-device support that's a available in e.g. Matrix.
They don't, and I think they argue it's a security feature.
It is, at least, intentionally designed that way, for better or worse.
You can get per-conversation sync by joining multiple clients to the conversation.
It's one of those things where you'd probably want to be less secure and always sync to all devices.
https://simplex.chat/docs/server.html