This screenshot looks better than the other of yours, but honestly I think it's more due how how antialiasing is rendered there vs in your Firefox screenshot.

Additionally, for ages Linux had shipped with Full hinting, which means distorting the font so straight lines are always on integer pixel boundaries, which looks atrocious. These days distros like Fedora use Light hinting, which is a little better, and in my opinion No hinting looks best, which is what macOS does, but on a low DPI screen means having blurry font. So on low DPI screens you have the choice between distorted but clean fonts, or undistorted blurry fonts.

I don't know about sway, in my case I'm using Fedora with 2x scaling, so I have the option of disabling hinting and avoiding distortion.