The only thinning I could imagine are to separate the plants and space them out. I think to do best, the plants need to be at least six inches apart. I would expect that if you have a lot of plants growing on top of each other, competition will be such that they won't produce full leaf heads. I've got a large pot with four or five plants with that spacing.

Just snip the seedlings and use them!

I will thin them a bit, I think - I do always grow it in large pots a bit crowded - they sort of thin themselves into maybe 2" spacing IIRC. It won't do well in the ground here.

And I direct sow.

I thin mine. I usually sow mine by tossing seed in a 4” pot…. then once the seedlings are large enough to handle, I very carefully separate and repot them individually. Just don’t break the tap root, and cover with potting mix only up to the cotyledons.

eta: if you mean for spacing, then yes too. I find that a single parsley plant grows very well in a gallon pot. Two or three in a gallon pot don’t do as well, so I try not to crowd them.