Just to share some useful information: there's an experimental feature in the ClipboardItem API that supports SVG images. As of November 2024, this feature is implemented in Chrome, Edge, and Opera. You can check the compatibility details here: Can I Use - ClipboardItem API (image/svg+xml).
For more details on how to use this feature, here are two relevant blog posts:
As of now, I'm not sure which apps currently support pasting SVGs, but the functionality is worth exploring!