Alright, I had looked at the download page and did not notice a download for Linux. After some searching I've now found the beta releases for Linux on the forum. The latest one is many versions behind the macOS and Windows releases, but it did run (although I do have this problem). Anyway, it wasn't my most important point, but it does mean I may find time to try out Unity's tilemap support at some point. :-)
About tile-heavy projects, note that Tiled is also a pretty decent level editor for levels that are not tile-based. I know the name may suggest otherwise, but you can work with shapes, points, polygons and arbitrarily scaled and rotated images to build your levels. The Sticker Knight example project demonstrates this very well. In Tiled 1.2, many usability improvements have been made to this area and I do plan to expand on that in future versions as well.