Actually, if you stir the mix, it'll probably compost. Ground up leaves will as well. Not entirely clear what you're trying to achieve, though. As noted, not smart to plant in compost, especially in a container. As to ground up eggshells, they're just ground up carbonate rocks. They won't do anything. But if you want to throw in rocks, that's up to you.

I've used Starbucks coffee grounds in a BIG, three-section compost bin system. They are a real asset for a compost system, (Red Worms are especially attracted to them,) but I think your ratio of grounds to other things is way off.

I agree with having the big pile of lots of different 'stuff'.

I also agree that you don't plant in compost, but rather soil that has been augmented with compost.

My sister has been growing wonderful things in outdoor pots full of compost every summer for about 25 years. Herbs, salad greens, eggplant, and some others. She makes compost of all kitchen waste, garden waste, and autumn leaves.

I've tried composting in an intact large bucket/small drum, and it went anaerobic and stinky. For good composting you probably want drainage in the bottom, and ideally to turn the compost a couple of times during the process.

For a single season growing annual plants, you can get by with just compost. But it is ill-advised for anything longer term in a container. Compost is never really finished so it will continue to decompose and degrade (and shrink) over time. And that will adversely impact the container drainage if even just a small part of the container mix. And compost has limited nutrient capacity and will be missing the necessary minerals or trace nutrient elements that real soil provides so one needs also to fertilize to get the best output.

Again, not a good container medium - but just for producing compost, use leaves with your coffee grounds rather than (or in addition to) paper. .As others have noted, paper tends to turn to sludge because it absorbs water so quickly and reverts to pulp. But fall leaves and coffee grounds are a classic combination and a favorite environment for worms - so make sure there are holes for drainage and to let the worms inside.

My thought on this is that if it's lots of coffee and there are leaves, just mix them up and use as mulch or leave on the ground. Or compost for however long is practical at first - a big pile of coffee grounds and leaves is sufficient. But within reason (not super thick layers), coffee grounds directly on the soil (lightly raked or hoed to mix a bit with soil) becomes indistinguishable pretty quickly. YMMV depending on climate, I know some say coffee that dries too much can become crusty and hydrophobic, I don't have that problem. I've put coffee on lawn and lightly raked, within days not noticeable.

TL/DR version, it may not be necessary to compost coffee at all - just apply. Note, NOT saying to use in containers.