They dried out? They got too hot? Damping off? I really don't know. But, like the fennel and dill, these two would also be easier to grow if sown directly outside. Growing under lights adds a mass of complication to starting hardy vegetables.

Do the cups have drainage? Can't be too much light. How hot? Why a heat lamp?

@floral_uk z.8/9 SW UK you are right of course but I have some issueS in directly sowing outside that is why I take this route of starting inside. One of those issues is that I have many cats and they are not yet used to me doing veggie gardening. Every time I dig or move earth in any way they come in after me and dig everything back up to check whats going on. They have so far defeated every barricade I have tried. When I plant larger plants and mulch heavily around them then the cats tend to leave them alone, but not always. I am hoping the novelty of my digging will wear off in a year or two. But we just got two new kittens.

@robert567 yes the cups have great drainage, I will post a picture. The heat lamp makes the room a toasty upper 70s. Meant to make you feel warm when you are going in and out of a bath/shower and can be cut off quickly. Without the lamp the room is 65-70. I am growing tomato, pepper and eggplant (+other warm weather) seedlings in the room as well. Someone here had suggested that if the area is warm such seedlings will do better. Thats why the heat lamp and it is way up in the ceiling. But I am thinking the heat may not be the issue.

Yes, I understand it can be hard to overdo light but it can happen. last year was the first time I started using grow lights. YT videos said to bring in the lights very close to the germinating seedlings. About 2 inches above them, especially for peppers and eggplants. I did that and my pepper and eggplant grew funky and looked sick. The roots however were good. I started over from new seeds and moved the lights further up and everything grew great. It is ofcourse a matter of the light output of the lamps being used. I think I have very strong ones. I did not know quantitatively what I should be aiming for.

Wish I could figure this out.

@daninthedirt (USDA 9a, HZ9, CentTX, Sunset z30, Cfa) good question Dan. NO the stems are not hurting at all. Not even when the leaves are dry and dead. I dont think the soil is sterile in a medical sense but they are reputable brands and from brand new bags. And all my other types of seedlings are thriving in this grow mix. I dont think heat is an issue anymore. I cant figre this out yet.

Is there any reason why these seeds will not want to grow in a small pot after germination?

FWIW, https://www.smartgardener.com/plants/571-mustard-greens-mizuna/diseases/797-damping-off. I always look for stems rotting with damping off, but this Mizuna-specific reference says that other kinds may cause tops to die back. Also, I understand that some plants are more prone to damping off than others, but I've never seen any actual lists. I've heard of damping off being a problem with people using coco-coir for germination. Not sure why that would be.