I am wondering is it correct to say "I ate one soup today. I didn't eat much."
That is not the way a fluent speaker would usually phrase that idea.
"One soup" could mean "one kind of soup" but it would not normally be used for "one serving of soup". The idea could be conveyed by any of:
- I ate one bowl of soup today.
- I ate one serving of soup today.
- I ate one can of soup today.
- I only had some soup today.
- All I ate today was one bowl of soup.
"One soup" suggests several soups, but when "soup" is used to describe an amount of soup eaten it is not a count noun. When it is short for "type of soup" it is a count noun, as in "I learned how to make four soups in cooking class." When a noun is not a count noun, it does not get modified by a number. We don't say "He delivered one sand", but instead "He delivered one bag of sand" (or "truckload" or other quantity in place of "bag".)
This could be acceptable in an emergency situation, e.g. after a major earthquake, you are stuck at home relying on emergency supplies, and you have only 100 cans of soup to share with your family.
Q: "What did you eat today?"
A: "I ate a cookie, 3 dandelions, and one soup today."
This would imply "can" as the unit of measurement, but is a very unusual way of referencing soup.
Under normal circumstances, you would say "I ate one bowl of soup" or "one cup of soup" or "one can of soup" explicitly.