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Likely, they have rotted. This article will help you to save them, properly:

https://www.gardeningknowhow.com/edible/vegetables/pepper/harvesting-pepper-seeds.htm

You can try dusting them with wettable sulfur. This can help to keep them free of disease as they are drying.

This is unusual, but serious. It appears to be Tomato Spotted Wilt Virus. Viral infections, like humans, cannot be cured- It can only be treated. This one will take hold of tomatoes peppers, and any other closely related species.

The soil is bad. It should be disposed of, well, away from your property. Should this spread to your outdoor soil, or any other soil that you use, regularly, you will likely face a permanent viral infection in your soil. It won't harm you in any way, but you will never be able to grow any plant in the area that can be infected, should this happen.

The pepper is still edible, but that plant needs to be destroyed, quickly.

https://www.gardeningknowhow.com/edible/vegetables/tomato/treating-tomatoes-with-spotted-wilt-virus.htm

There are a few oils that work, but I would recommend a nifty little bacteria called Bacillus thuringiensis (Bt). It is harmless to you, but will make quick work of the caterpillars.

Here are some articles that will help:

https://www.gardeningknowhow.com/lawn-care/lgen/tropical-sod-webworm-control.htm

https://www.gardeningknowhow.com/plant-problems/pests/insects/tent-worms-control.htm

They are small structures of plant tissue that resulted during the seed-making process. They are edible if you want to include them in your salad tonight. I don't know if they would grow properly like a seed, but you can try planting one and see.

Here is the advice we give about planting seeds from store-bought peppers:

https://www.gardeningknowhow.com/edible/vegetables/pepper/store-bought-pepper-seeds.htm

They are, simply, stressed. You can trim them and repot them into fresh soil and compost and it will, likely, return to a more normal looking state.

https://www.gardeningknowhow.com/edible/vegetables/pepper

They look like they need more water. They are very small yet and may need water every day. I wouldn't saturate the whole pot, though, if they are in large containers.