Should I separate files in After Effects for different part of a Premiere Pro project?
You can do both. I myself have used both methods. However, my recommendation would be to do each shot in its own project. Here are my thoughts on both methods.

Doing it all in one project makes things faster, because you don't have to create a new project for every shot you have. However, the problem with this is that the project gets really convoluted. It means you have to be super organized to keep the project tidy. But even when you do that, if you need to come back to the project, it usually takes you a bit of time to get your head around what is what and where can I find this specific item, especially if you are using a lot of precomps in the project.

Doing each shot in its own project keeps things really simple, because you know that everything here belongs to this shot and that's it. You can quickly figure out what is happening, especially if the project is organized and tidy.

Of course, I am assuming that you are doing simple effects on each shot. If you are doing major vfx or compositing work on your shots, then you should definitely create a new project for each shot, because that project will get convoluted due to the scale of the job you are doing. So you shouldn't be making it even bigger with adding other shots to it.