As you run by items, should they just automatically get picked up and sold? Or just enter 1 giant spreadsheet so you can use or access the value of anything you’ve been near?

Of course not, picking stuff up gives you a dopamine hit, which is the entire point of playing video games in the first place. If everything happened automatically then you're right, it would be pointless. People also want to keep/sell different things.

Should you even be able to pick up a plate or should only core items be actual items like old school games?

Yes, Some people like setting up the random stuff in their house for aesthetic purposes or to screw around with the game physics.

Not having a carry limit is not the same thing as having automation. Inventory management is not part of the fun. Imagine watching a game dev presenting their new game and they highlight the carry limit as an exciting part of the challenge. It's asinine if you're going to have a game where hoarding shit and needing a ton of materials for crafting is a major part of it. Limit what gear you can access at once if you're concerned about having too much available to the player messing up the challenge but the miscellaneous shit? why?