Ok, so SS does not make this easy so here's the solution:
After uploading your .svg file as a link, you will get the dynamic path:
/s/image.svg
Note that this dynamic version WILL NOT WORK: background-image: url("/s/image.svg");
Paste this after your url:
https://exampledomain.com/s/image.svg
This will redirect to a very long file path.
Copy that new url and use it in your custom CSS as the path:
background-image: url("https://static1.squarespace.com/static/60cbad31bb9e2415f759b216/t/60d1116d41b3160fdcad630f/1624314221425/image.svg");
You should be able to use this version as well, but keep in mind if your url changes or is in beta:
background-image: url("https://exampledomain.com/s/image.svg");
Really. All of this for a common file type like .svg 🙄