Unfortunately linked accounts don't count as primary devices so you will always have to keep the original device active or else they'll eventually delete your account.

I believe Signal last year started allowing you to backup your primary account and transfer it to a new device?

Yes but that's different than linking a device. Moving it to a new device deactivates the old one. You can only have one primary device and you must log in with it every so often or else your account gets deleted.