There's a third party appimage, still on 1.3.1 though: https://github.com/pkgforge-dev/ghostty-appimage

Normally not a fan of appimages, but this group focuses on making higher quality versions that make very few assumptions about the host system and work almost anywhere. While also prioritizing speed, small sizes, and up-to-date dependencies.

you should be able to get it from your system package manager or flatpack. linux is annoying here because it's a GUI app.