What's the best way to run software on an old Ubuntu system that I don't want to upgrade or run apt-get on, and I don't want to run stuff inside a Virtual Machine, and snap is broken, and docker as well? Compiling stuff seems too much trouble because of all the dependencies. I was hoping for Nix to save me here, but it only compiles for a specific libc version.
You can download precompiled binaries of a lot of things from git these days. You can modify your PATH to include a location of your choosing and put the binaries there. It probably won't work well though because you'll be missing dependencies.
You could also chase down debs, download those and install them manually and specify your install path. (I don't have the deb switches memorized, so many pages are your friend.) You'll have dependency problems here too but you'll get friendly warnings that can help you hunt down other missing packages and you can work your way up from there. It won't be fun.
I'm glad I started in Slackware and used it for about 15 years as my daily driver. I'm comfortable with Linux The Hard Way and when people tell me how hard it is to run Linux because all the weird kinks, I just chuckle.