Check your obsidian.desktop file. I use Garuda, and it is in ~/.local/share/applications. It should have an Icon=path/to/icon/image in the file. If it doesn’t, you can add it to the file. I have attached mine as a .md file for reference.
Obsidian Desktop File.md (1.3 KB)
Also, I use appimagelauncher rather than the shell.