I know the protagonists, after their adventures, disappear from the public eye. Bethesda does this so that any protagonists you make can be considered canon. For example, the eternal champion just kinda disappears from the public eye, the agent dies, the nerevarine sails to Akavir, the Champion of Cyrodiil transforms into Sheogorath, Cyrus is a fixed character, so he doesn't really have that problem. My question is, what happened to the other protagonists (aka, the protagonists of the spinoff games)? Specifically, the apprentice, the master tunnel rat, the hero of dawnstar, and the soul of conflict? Considering no one really cares about the spinoff games, I had trouble finding information about them.

You are the protagonist, therefore they end up wherever you want them to. That's why you can't find information on it, it's intentionally left ambigious.