Finder, small svg preview

Install the free Inkscape. Then, single-click an arbitrary SVG icon and press option+cmd+i to expose the Finder's Get Info window. On that panel, will be an Open With section, where you set the application to Inkscape and then click thru Change All… The ghost SVG icons will now show their true artwork, provided your Finder window has its Show icon preview selected.

And in the your Assets folder shown in Finder, press cmd+J and then select Show icon preview.

Apple's Preview application does not yet support SVG artwork in macOS 13.4.1, and you may need to right-click on an SVG and choose open With to select a different tool to open the SVG as a double-click will likely open it in Inkscape.

Update macOS from 13.0 to 13.4.1 and see if that makes a difference. Never fall behind in your operating system updates.

That Inkscape.app needs to be installed in your /Applications side bar in Finder, not left in the installer, if that is the case. Note that my Open with entry is different:

Either the application that created these .svg has produced versions not compatible with Inkscape, or what you see is really all you will see in the Finder. Stating that mine works fine is little consolation to you.

When you changed the Open with application to Inkscape, did you click the arrow indicated box and click through its subsequent dialogs? If you didn't do this, Inkscape will not be assigned as the default opening application for those .svg items.

You are welcome.