'Sync your settings'

I am unable to sync my desktop and laptop. My desktop reads, "Some features are only available if you are using a Microsoft account or work account" and 'Sync settings' is off and greyed out. My laptop has 'sync settings' on. Both devices are set up the same way and I have the same Microsoft account for each. Both were synced once upon a time because I had the same background on both. I am unsure whether the change might have occurred when I updated both devices to Windows 10 last year. I appreciate there might be many reasons for the latest situation that will make the cause difficult to identify, but one suggestion or another might just help.

Brink
I have a Microsoft account; I signed into it just now. My laptop is recognised but not my desktop. I do not know the significance. I clicked, "Can’t see some of your devices? Check for others" in https://account.microsoft.com/devices. "We didn’t find any other devices. Add more devices" followed. Next,
"Windows 10 PCs
Add your PC to use Find My Device and get support for it
To add a Windows 10 PC:
1. Go to Settings > Accounts > Your account
2. Select Sign in with a Microsoft account instead
If your PC still isn't showing up, try adding the Microsoft account again."
"Your info" shows, not "Your account" and "Sign in with a local account instead".
I am at a loss.

swarfega
I see nothing relating to 'verify' in Settings/Accounts. I returned to the Microsoft "Sign in" page which takes me to https://account.microsoft.com/?lang=...ignedout-index where I am greeted with "Hello!" and my personal details appear.

Brink
I thank you for your reply and attempts to help. I fear I am stumped: My laptop is Windows 10 Pro but my desktop not. I have resisted carrying out any work to the registry ever as it takes me beyond my comfort zone. I do find the issue confusing, however, as I commented in my opening post: the background on my laptop would change automatically when I changed it on the desktop, once upon a time.