Personally, for my uses, I’ve found that having a pickup object that is destroyed is an appropriate solution. This way, you don’t leave behind any “ghost” actors that don’t do anything and can’t be seen. However, that’s all for the sake of keeping it neat. A ghost actor like that isn’t really going to impact the game in any way.
Both of these methods are perfectly valid and will work quite well. It’s entirely up to you which one you choose to do, and which you’d prefer implementing. If you think you can do the second option faster than the first, go for that one. If there’s something about your inventory system that makes the first option preferable, do that instead. There’s really not a wrong answer here.