I mix it with water and press it into a small soil blocker
That stuff should be ok. I'm not familiar with it though, and it may be too fine and/or too tightly packed maybe. I'm not a fan of commercial "germinating" mixes. I find that they're too fine and either lock up or dry out too quickly. Or the fertilizer in them is too strong. Johnny's seeds has a nice compost based commercial soil block mix if you're in the US. Vermont Compost Co's Fort Vee mix is all I ever use for my blocks. Good stuff. Well, except for the weird marble chunks, ya have to fish those out. For regular seed starting in cell packs or trays I just use Pro Mix BX. And I don't start feeding the seedlings until they're already leafed out and pretty high. (If I do at all.)
If you're using one of those soil blockers that make the half inch cubes, that may be a problem. Some seeds are very picky about sowing depth and having room for their roots. Onions especially are not compatible with 1/2 inch blocks because they need to be planted a half inch below the soil surface and then they send a rootlet down first before sending the stalk up. If the rootlet hits bottom, it's game over. They stall out. Maybe try germinating in a bigger soil block (I like the 1.5 inch blocks- it's a good size for most) or just using a regular 6 pack.
For years I ignored pepper seed planting depth recommendations and then had problems with the mature plants toppling over in the garden. Once I started
following the directions on the seed packets that problem went away. Imagine that!
It's a T5 bulbs with a 6400k full daylight spectrum.
That should be fine. T5s are da bomb. I love mine. But they do get roasty and for most stuff you don't need a heat mat with them. (Heat mats raise the ambient temps by 10+ degrees. So under T5s they can reach 80+ degrees easy. And fry your seedlings.) And you don't need T5s to be as close as other lights starting out. I generally start them out at about 8 inches above the trays before germination and raise them after first true leaves. By the time the plants are 4-5 inches high the lights are 16+ inches above 'em.
It's hard to guess what goin' on. If stems are collapsing at the soil level you could have Damp Off from contaminated soil or from over watering. As noted, leggy stems usually mean not enough light, but that's unlikely with the T5s.
One thing I do after the seedlings are up is I set up a small fan to blow over them for a while. Like a half hour or so daily. That strengthens stems as they grow and keeps everyone from getting too soggy.
The biggest issue for seed starting indoors for me is the timing. I've found that if I start some seeds too early they just don't do well (even when they're big and look great) when they're planted out. So I try to keep their time under the lights at a minimum. The sooner they get outside and in the soil the better. Even if they're pretty small.
Final thoughts: You may want to try what's called "winter sowing". (And you can probably still do it now.) Basically you make mini greenhouses out of cut up milk jugs, load them with soil and sow your seeds and then set them outside for the seeds to germinate at their own pace. There's lots of info about it online. It works really well for natives and perennials that need a cold period before germinating. And it's kinda crazy fool proof. The other thought is that some plants really prefer to be sown directly in the ground under natural conditions and no amount of coddling them under arifical conditions is going to work. Hope this helps. Good luck!