Don’t bury them. They’re more like a tomatillo than a tomato or pepper - no fuzzy stem.
I think Flea Beetle is your problem. Since they ARE a beetle, you may need something stronger than neem or soap. Can you get Captain Jack’s Dead Bug Brew by you? Bonide makes it. It contains Spinosad, if you can’t find it and need a substitute. (Approved for organic gardening...)
I have some Sevin I will use on my seedlings.