I have a 2013 MacBook Air, which I didn't use for a couple of years and then decided to convert to a Linux Mint machine.
Later, I decided that I should re-install MAC OS Lion and successfully upgraded to Big Sur.
Now I dual boot between Big Sur and Linux Mint.
I set up Time Machine on a Share on my Synology DS216Play NAS.
Time Machine says it is backing up and when I look at the Share via Windows 10, the .sparsebundle says 8.26GB.
I have used 'Connect to Server' and it connects to the NAS via 'afp://DS216play._afppovertcp._local'. I then select my Share i.e. 'Time Machine Folder'.
But when I 'Enter Time Machine' everything is empty for 'Desktop' and everything else in the past.
Time Machine has never given any error.
I have used Time Machine in the past and to the same NAS and there were no issues.