New Catalog copied everything on my desktop

Also, in your Finder screenshot, on the left, the folder named Photos. What is in it?

In your screenshot of Finder, looking at the contents of Desktop. Showing that folder named Lightroom. Note the catalog in it (Lightroom.lrcat) What happens when you double click on it?

No follow-up by @Elizabeth26977484xo95  ?

I note there are two catalogs in use!-

1) One on the desktop,

2) Location unknown with a different name-

And for the error message-

"Destination is not writable" is commonly a permissions problem

Follow the advice in- FULL DISK ACCESS -MAC 

The catalog file usually goes in the Lightroom folder under Picture. However, it really doesn't matter where you put it, this is not the cause of your problem. When you import photos, you have a choice of "Copy" or "Move" or "Add" (Add meaning the photos are not copied or moved, they are left where they are). You ahve to decide which is best for you. If you choose COPY then it will make actual copies of photos.

Also, I point out that putting photos or catalog on the desktop of your computer is a particularly poor choice of location, catalog would be better in the Pictures folder and photos would be better in subfolders under Pictures; or subfolders under some other parent folder — many people put the photos on an external or second internal drive.