I hope if and when you get a seedling that you plan to keep it permanently in a container. It is a terrible thug in the garden.

I am surprised someone wants to grow mugwort (wormwood) - it is a constant battle keeping it out of my garden beds.

But, because of that I have become educated on mugwort propagation, and they usually don't grow from seeds. They sprout from rhizomes that form on the roots - which makes them so difficult to control. If you leave any of those little rhizomes when you pull them out, you will just have more in a few weeks. I'm sure they can be grown from seeds, but the seeds don't need a high germination rate because the plant can spread just fine without them. I would see if someone sells the rhizomes and try that instead of seeds. Or find someone that already has a mugwort plant and get a few rhizomes from that.

Mugwort does need to cold stratify, so if you haven't given it a cold period, relegate it into the garage for a few weeks for a cold period, then bring it in. I don't think freezing is necessary, just a cold period in the upper thirties, low forties-ish. All my cold stratified stuff just goes on the garage wall where it can get cool to cold.

It also requires light to germinate, so surface sow it (although it's less touchy about this part). Shallow sowing is usually just fine for these.

And yes, restrict this to its own pot, mount automatic flamethrowers around it, and threaten it regularly with dire action should it try to escape. Deadhead the blossoms to avoid getting seed in your garden.