Hey Saeroner. Your seedings still look okay, but that soil mix won't work for peppers and the issues will get worse over time. Topsoil isn't growing soil and backyard dirt in south Florida isn't likely to help any.
My recommendation is to buy a bag of quality "container" soil from somewhere other than Home Depot, preferably a local nursery, and confirm with them that it's suitable for container growing plants such as peppers and tomatoes. With the new soil, transplant them into containers roughly Solo cup sized. Those sprouting cubes they're in should pop out easily if they're not too wet or too dry, so I'd try to to catch them when they're very slightly moist and pop them into new homes without disturbing the root ball. If you end up disturbing them some it's probably no big deal, but less disturbing is generally better. Keep them out of the direct sun after transplant for a couple days.
After transplant, expect the existing leaves to look no better and likely worse. Some of the cotyledons may even drop, but hang with them. Expect a bit of a pause as they adjust and root in, but once the new growth starts coming in it should be greener and healthier and you'll see that they're back on track. After their roots fill out the new, slightly large containers, they should be ready for their final homes.
Good luck!
