Any Photoshop gurus out there know if PS has a Pathfinder feature like Illustrator?

Pathfinder? Not really; but you could try getting creative with vector masks.
This can sort of act like pathfinder.

**If you happen to have illustrator
you can always import objects into photoshop as smart objects and keep the pathfinder functionality…

What would be the purpose of this? Or rather what is the desired end result? We may be able to tailor a better suited answer for you based on that.

I’d go with “Merge visible” or just “select/fill” or something. Like tWrex said, it depends what you’re trying to do/get/achieve.
You can just select the shape you want, then switch to the other layer and (delete/fill/copy/cut etc.) not exactly the pathfinder but eh…it’ll work.

I would like to be able to merge shapes, yet not have them flatten/rasterized so I can more easily adjust the shapes later on if needed. I’m a little surprised PS doesn’t have this ability, but I also understand that it’s not meant for that type of object either. Thanks for all the feedback!

I’d go with what @blastfamy said then. Use vector masks.