Contemplating using compost

So with this whole COVID. I have been struggling to get my nutrients. Well actually I don’t leave the house really. So I’m thinking about using compost.

I don’t want a huge compost bin and am considering using one of those small ones under the kitchen sink. Can I just throw scraps in it and leave it for a long time and then use it in my soil? is there anything I need to look out for? Do I need special living soil grow bags or can I just use the current honor fabric pots and vivosun ones I have?

Do it. Compost. Check out composting worm bins. Then you get worm castings and tea. You can't just leave it in a jar because it takes awhile to break down. And it Will smell as it breaks down. Best to do it outside. Make a pile, add dead leaves, add fresh green materials, and give it a good stirring up with a shovel a few times.
You can't add dairy or meat to aerobic compost. Check out Bokashi. Japanese composting type that is anaerobic.
Nature figures out a way to do what it needs to do. If you can do it outside, somewhere, it will be easier.

You'd be surprised how little meat you need to compost; keep the meat scraps down

Bokashi is I think what you are talking about. Not sure what kind of space you have under the sink but even just a 3 tray worm factory will give you active castings for life.
The benefits of having a worm bin cannot be understated. My grow is pretty much self sustainable. I do need to buy more fertilizer and a few soil amendments annually but most times I just add compost and D-lime to recycle the mix. The worm bin itself has no “stink”; it is more of an earthy humus smell but I do get a few gnats flying out of there every so often. They are easily quelled by a light dusting of diatomaceous earth.
I throw in all the cannabis leaves from harvesting and any organic kitchen scraps like veggie skins, coffee grounds, eggshells, or rotted fruit. The leacheate that oozes from the bottom spigot is liquid gold. I dump it on plants late in veg or mid bloom if they need a boost. House plants and cacti get the leftovers. Must be diluted by half; it’s kind of hot as is.

Only thing I'll add is this close to season bokashi may be the only viable for this year's use. I'd get a worm bin going now so it's ready for next year ahead of time.