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What is happening to the peppers, in terms of symptoms? If we know what the symptoms look like, we can better diagnose what is causing it. In the meantime, give them more water with a bit of sugar, as it's possible they are suffering from transplant shock.

You may simply have a pollination issue. Pepper plants can shed the newly formed blossoms/fruits if the growing medium becomes too wet, too dry. Pepper blossoms are even more sensitive to temperature fluctuations during pollination. When night temps fall below 58 degrees or daytime temps rise above 85, the blossoms or fruit can fall off.

Cool soil can do this to peppers and bells tend to be more affected by cool soil than hot peppers. Ideally, the soil (not the air) needs to be above 55F before you plant peppers. The warmer the soil, the better they grow. There are even some who believe that if peppers are exposed to temps under 50F, they will not produce well.

You may want to wait a bit longer in the future before putting them into the ground.

You can also try giving the plants some potassium and phosphorous. Soil lacking this can create stunted and deformed fruit as well.

Depending on the variety, you may see your first sprouts in about 7-14 days, but some peppers can take as long as a month or more to come up. Pepper seeds are notorious for taking their time to germinate, or germinating at different times. Also, peppers won't even attempt to sprout if temperatures are below 60 degrees F. So don't give up!

It is likely a rodent of some kind, possibly rabbit. They would not be going after the leaves of the plant, but rather the flowers. Does this happen right as the plant is flowering? Peppers are nightshade plants, so the leaves are poisonous to most animals, but not the flowers and fruit.

I would treat the issue as a rodent problem. You may find these articles helpful:
https://www.gardeningknowhow.com/plant-problems/pests/how-to-keep-rabbits-out-of-gardens.htm
https://www.gardeningknowhow.com/plant-problems/pests/animals/garden-mouse-control.htm
https://www.gardeningknowhow.com/plant-problems/pests/animals/vole-control.htm

It sounds like it may be a pollination problem. Give your peppers a little shake every few days to help loosen up the pollen and also avoid using blanket pesticides, as these can kill both the good and bad bugs in the garden.

Whatever you are using on the tomatoes is good for the peppers. Tomatoes and peppers are from the same plant group and are related.