Create an app including binary/library dependencies
I have an old application, EagleCAD, from 2014, a 32bit app, I managed to install it on my linux (Debian based, 64bits) and it works fine, but I had to look for and install some lib manually.
How can I package all this, the bin and libs, into one that I could easily re-install on about any distro? AppImage? Flatpak? Snap?
You should be aware though that distros are starting to remove 32bit support in general, as in compiling their kernels without it so it will not work for many years longer.
Copy all the libraries into one folder, then make a wrapper script using the LD_LIBRARY_PATH environment variable pointing to that folder before starting the application.
The modern way to run 10 year old binary applications is "don't", all of the technologies you listed are designed with a security focus and that means regular updates.
Essentially, it's the same thing that you're doing, just automating getting the dependencies, and then copying everything in the lib-your-executable dir to your LD_LIBRARY_PATH. I don't know of a better way, other than statically-linking the binaries.