Having this functionality natively in Obsidian would be the preferred way for me too, meanwhile, one of the easiest but most feature complete approaches is to use the following snippet with the excellent obsidian-user-plugins.
No need to create any files, just install the plugin, activate it and paste the following code into a new Snippet:
plugin.addCommand({
name: 'Copy WikiLink to Clipboard',
callback: () => {
const noteFile = plugin.app.workspace.getActiveFile(); // Currently Open Note
if (!noteFile.name) return; // Nothing Open
// Copy WikiLink to clipboard
navigator.clipboard.writeText("[[" + noteFile.basename + "]]");
}
});
You can then add the new command to any place where commands can be added, including hot keys, menus, sidebar, etc.
This is vey basic and assumes unique file names in the Vault resp. does not put the path of the file within the Vault in the WikiLink. If you need something more feature complete you could expand the code quite easily to test for duplicate file names under different paths and then copy the WikiLink with the path in the Vault or to copy the path in any case and use the display title feature of the WikiLink Syntax.