My cat keeps bringing me 'gifts'—should I be worried or flattered?

So my cat, Luna, has started this adorable (but slightly gross) habit of bringing me little 'presents' from outside - mostly leaves, twigs, and once even a tiny, lifeless bug. It's like she's trying to share her hunting prowess or maybe teach me how to be a better hunter? I’m torn between feeling flattered and a bit ick.

She’s always so proud when she drops something at my feet, looking up at me expectantly. It’s such a sweet bonding moment, but I wonder if this is normal cat behavior or if I should be concerned about cleanliness or safety. Has anyone else’s pet done this? How did you handle it?