The background on my laptop did not change when I chose a new background for my desktop recently. Both machines have been synced for a long time without change. "Sync settings" is "On" on my laptop. My desktop, however, has a message,"Some Windows features are only available if you are using a Microsoft account or work account." in red, the names with their buttons are greyed out and "Sync settings" is "Off". My Microsoft account has been set up and remained constant as far back as I can remember. I use its password every day to sign in to both machines.
NOTE: When opening my account at https://account.microsoft.com/, my laptop alone is registered. I do not remember this being an issue previously, however. In any case, registration choices appear to be limited to Microsoft products such as Surface, XBox, Surface Book and Microsoft Band.