Strictly speaking, you have already given the answer to your question:

Separating the seedlings would lead to many more plants than I can probably afford in terms of space...

In that light, the answer would be to kill all but the strongest seedling of each cup.

If have enough space to accomodate some more peppers, you could carefully try to separate the seedlings after they have grown one or two pairs of "normal" leaves, and plant them into their own pots.

How to do this? There are different opinions on that. Some recommend just separating the plants by cutting the roots between them. However, I generally try to hurt the roots as little as possible and gently wiggle them until I can easily separate them. This might be preferrable with such a small distance between the plants as otherwise you could risk cutting too much of the root system. This question offers some more insights regarding that.

Strictly speaking, you have already given the answer to your question:

Separating the seedlings would lead to many more plants than I can probably afford in terms of space...

In that light, the answer would be to kill all but the strongest seedling of each cup.

If have enough space to accomodate some more peppers, you could carefully try to separate the seedlings after they have grown one or two pairs of "normal" leaves, and plant them into their own pots.

How to do this? There are different opinions on that. Some recommend just separating the plants by cutting the roots between them. However, I generally try to hurt the roots as little as possible and gently wiggle them until I can easily separate them. This might be preferrable with such a small distance between the plants as otherwise you could risk cutting too much of the root system. This question offers some more insights regarding that.

Strictly speaking, you have already given the answer to your question:

Separating the seedlings would lead to many more plants than I can probably afford in terms of space...

In that light, the answer would be to kill all but the strongest seedling of each cup.

If have enough space to accomodate some more peppers, you could carefully try to separate the seedlings after they have grown one or two pairs of "normal" leaves, and plant them into their own pots.

How to do this? There are different opinions on that. Some recommend just separating the plants by cutting the roots between them. However, I generally try to hurt the roots as little as possible and gently wiggle them until I can easily separate them. This might be preferrable with such a small distance between the plants as otherwise you could risk cutting too much of the root system.

Strictly speaking, you have already given the answer to your question:

Separating the seedlings would lead to many more plants than I can probably afford in terms of space...

In that light, the answer would be to kill all but the strongest seedling of each cup.

If have enough space to accomodate some more peppers, you could carefully try to separate the seedlings after they have grown one or two pairs of "normal" leaves, and plant them into their own pots.

How to do this? There are different opinions on that. Some recommend just separating the plants by cutting the roots between them. However, I generally try to hurt the roots as little as possible and gently wiggle them until I can easily separate them. This might be preferrable with such a small distance between the plants as otherwise you could risk cutting too much of the root system. This question offers some more insights regarding that.