Treating this as an X/Y problem ... do you separate your waste? I separate anything that smells (non-compostable food waste, non-recyclable junk) into a separate pail, that is emptied every day or two, so it's never there long enough to get smelly. The dry recyclable stuff can stay in there as long as it wants, and the compostible stuff (waste vege material) never really smells too bad, but again gets tossed more frequently.

Compost, and then recycling (paper/tins/glass mixed where I am) and rubbish in two bins in the same drawer thing.

That's part of the problem really - after compost and recycling I'm left with very little waste, so anything that there is can sit there a while. I tend to empty it because it's been there a while rather than because it's full.

You could make the bin chew with it's mouth closed and just vibrate in time with chewing. Might also help to settle some of the material.

Maybe try feeding it some baking soda every now and then to knock-down the odors?

Edit: Activated charcoal works too! It can be found at pet stores.

Decrease closing speed

Hmm, you could install a small fan that kicks on when the drawer is open/closed to pull air from the interior and exhaust it into an adjacent airspace, maybe through a filter if that adjacent airspace is still the room you are in.

Make a lid that goes over the top of the trash so it's contained when pulled out. Manually removing the lid (or however you modify it) will be less dramatic than opening the drawer.

Have the lid slide or pivot to open laterally?

Take out the trash?