What does com.apple.timemachine.supported denote? What does the presence of a file named .com.apple.timemachine.supported denote?

Is it safe to delete?

I find about a dozen of these scattered across my local hard disks, not the TimeMachine volumes...
It means that the folder it is in is supported as a target for Time Machine backups. They are very tiny files and wouldn’t be a space hog. But if you are seeing them, you are probably seeing other hidden files as well. But if you are using Time Machine for backup, don’t delete these files or the folder/disk wouldn't be able to be used as a Time Machine backup target.