they all died when I transplanted them individually in pots. I am using a compost soil mix, a light brown type of soil. What could have gone wrong? I planted them deep btw, like 4 inches below to keep the roots moist but not drowning.
Not sure without having seen it and not quite following all the above. But they already weren't doing very well to begin with. I have never had sunflower seedlings wilting or curving like that. They were leggy (too tall and spindly) which is usually from not enough light. They were yellowing. And then you force fed already suffering seedlings super-concentrated fertilizer. The general principle is don't fertilize (especially with synthetics) plants that are struggling. It forces rapid leaf/stem growth, when what you want is for them to heal, get sturdier, with better root systems. All that before you transplanted them.
"Compost soil mix" You mean a mixture of compost and topsoil? Seedlings in little pots need to be in potting soil, which is light and fluffy and very well draining. Light brown soil is usually dry, if moistened it should be dark.
"I planted them deep like 4 inches below" Below what? If you buried the stem 4" deeper than it was before, you likely just rotted the stem out. We bury tomatoes deeper because they have the interesting (and fairly unique) property of rooting all along the buried stem. Most plants do not:
"When you do plant your seedlings in the garden, do not plant them deeper than the level that they were previously growing. Planting them deeper could harm the stem and deprive the roots of essential oxygen."
That was not written specifically about sunflowers, but it applies.
How were the roots looking when you transplanted? Did they have healthy root systems? Did you handle them gently in the transplanting process? Did they get watered in gently, but not left soggy? Lots of things can go wrong in there.