Agreed -- those are normal roots. I usually plant the pepper seedlings deeper. Not quite as liberally as tomato seedlings but a little bit deeper. In the pictured seedlings, the bottom of the stem where it first sprouted, and where it transitions to roots is obvious (there is usually a little kink) so the root-producing cells were exposed. Luckily you did water well so this part wasn't dried out.
Bury to about 1/4" to 1/2" above where the roots are growing since the potting mix will settle. I'm a bit concerned about all those woody, mulch-y stuff. If your potting mix looks like that, it's not a very good one and may cause nitrogen lock up. Especially for starting seeds and little seedlings, I might even screen those out.
I usually add a little sand to the mix for burying pepper stems.