sharynworc wrote:
[...]
It's a 1TB drive, and the Mac Mini itself is 500 GB. There's about 20 gb available out of the 500 GB.
That right there is the problem. You have on appreciable free space available on the Mac mini's startup drive. This will cause all sorts of problems, including the issue of TM no longer backing up.
You need to find a way to free up a minimum of 50-75 GB of space on your startup drive. A generally accepted rule of thumb for giving macOS the room necessary to run properly is to always keep 10%-15% of the startup drive capacity free.
You can use another external drive to copy files from the Mac so that you can delete them and free the drive space. Consider moving your pic and vids first as those typically take up a great amount of space.
Also feel free to delete whatever you may have in your Downloads folder. If you found it once online you can probably find it again there if you need to.
This from Apple on the subject of freeing up space:
Free up storage space on Mac - Apple Support