What do you call the sheet (of fabric, nylon, etc.) that you lay on the carpet for everybody to sit around and have a meal?

Solution 1:

Consider, spread.

: a cloth cover for a table or bed M-W

Solution 2:

In English, the name for this item is the disappointingly generic "eating mat."

See e.g. Baluchi eating mat or soffreh from Iran or Afghanistan for an image.

Solution 3:

I've heard them called picnic blankets before:

The 6 best picnic blankets of 2021

This is used for outdoor occasions. For indoor, I would use the name for it in your own language, "We spread the / an X on the ground / floor before dinner." As you know, English can accommodate words and ideas from other languages. This often happens for foods, such as "hummus" or things such as a "hookah." You can call a "hookah" a "water pipe," but I think the original is much better.