I'm doing a challenge where I start with no money. So in order to eat anything, I have to buy the vegetables (such as lettuce) and eat it directly from my inventory. However, when I click on the lettuce, nothing happens. In fact, when I click on it and then move the cursor, the actually drags the lettuce even though I'm not holding down the mouse button anymore.

I also can't plant any alchemy ingredients. Whenever I click on one, no menu or interactions pop up. I just drag and drop the item as if I were holding down the mouse button.

This problem partially persists across multiple households. With some households, I can eat the food as long as it's dropped on the ground. But I still can't eat the food directly out of the sim's inventory.

Any idea what's causing this and how to fix it?

Do you have an outdated mod that affects inventory? Or it could be affecting something else and you're getting side effects from it.
It could also be a mod conflict.