Will a Gnome 4 snap run with Gnome 3?

The general answer to your question is: "Yes, a Gnome 4 snap should run with Gnome 3". Any snap should run on any linux system that supports snap. That is what the snap system is designed for.

This is at the core of these containerized application formats. They run in a sandbox, using their own libraries - or common libraries provided by other snap packages (the so-called "stage-snaps") that then should have been automatically installed with the snap, if not yet available.

What you are facing here is a defect snap package. Apparently it was published without sufficient testing.

Tl;dr:

This was probably a failed attempt at porting. Search the other channels of the same package for newer versions.If it is new, there is likely a nightly build, although I doubt you found this on stable. Check Flatpak for the same package. Chances are you will find it.

Conclusion:

It looks to me like you have a broken package? It is failing because it cannot find a shared library that it needs.

So technically, the answer is:

you need the file libportal.so

however..

1.) The fact that it is not included with eog or wrapped in package in apt is strange

2.) After a bit of research, it looks like the library is part of the flatpak api. In fact, the flatpak sandbox abstraction is sometimes called the "portal".

I am not a flatpak developer by any stretch, but I know enough to know that the sandbox implementations are way different to share apis.

My guess is that the package was recently ported from flatpak, and there is a discrepancy somewhere in the metadata for the package.

The gook news is that it is most likely available on Flatpak! Although if the app needs any significant permissions - i.e. access to the OS's devices or other global resources - to run, you will soon know what those differences I mentioned all too well.