Lightroom Backup

Keep in mind that Lightroom Classic backs up the current catalog, but not any of the images. So if you want to back up your original photos, you should also be using a separate backup method for the images.

That means one way to simplify this is, instead of relying on the limited backup feature in Lightroom Classic, you can maintain a consistent backup routine for your entire computer. Then you protect everything: The Lightroom Classic catalog, photos, settings and presets, and also anything else on your computer that might actually be more important such as financial and family records.

In other words, if you are already backing up your entire computer regularly, you don’t really need to use the backup feature in Lightroom Classic.

You need to give Lightroom full disk access. I'm not a Mac user, so I can't provide details, but take a look at this page.

https://community.adobe.com/t5/lightroom-classic-discussions/i-don-t-see-lrc-listed-under-full-disk-access/m-p/13587592#M311468

Other than that, you're a bit low on disk space, with 39 GB of 251 GB free.

It is recommended to have at least 20% free space. A full, or nearly full hard drive will cause lots of problems, so you should clear out some space as soon as possible.