Are they synced or not with the same account? Sync only works with one account that is synced only.

I am using the same sign in profile for each computer. Each computer shows the devices that are connected and signed in, but the password/login on the new computer says No synced logins found.

Maybe sign out of both and restart the computer and try again. Sync isn't instantaneous update sometimes it takes awhile for sync to sync across devices.