I'll look into serverside Last.fm support. I think it should be relatively easy to add. Agreed that an app would be awesome but I don't have the resources for it :(. The web interface works decently as a PWA (at least on Android according to testers, it has MediaSession support and stuff) but it's still kind of bad, definitely not a real app substitute.
For client side last.fm support the site could be added to this web-extension.