Hi and welcome! Sad to say, it wasn't the fertilizer that flattened those little seedlings, it was all that water in there. Your babies died of a bad case of damping off - the stems simply rotted. (it's actually probably a fungal process, so don't use that soil again)
That being said, you also don't need to add any fertilizer to seedlings until they are a lot bigger - those first two tiny leaves are called "cotyledons" and aren't the first set of true leaves that look like the ones the plant will have when it grows up. So until your seedlings produce their first adult leaves they are living on the food that was in the seed capsule and don't need any help. If they hadn't died of too much water, they probably would have burned from all that fertilizer.
Start again with some fresh, loose seed starting mix, in a pot or container that drains well. Then keep the mix just damp, about as moist as a wrung-out sponge. So if you touch the surface of the soil it feels moist but not soggy. Spraying the soil, or watering with a very fine drizzle will help to not break the tender stems of your seedlings.
When those first leaves appear, then fertilize weakly, and just a little bit every week or so. Use about 1/2 strength of what it says on the package, with a soluble plant food - pelleted fert like what you have in the picture is for your plants once they are out in the garden.
