It is not right to use 'many' or 'much' with percentage. It is that both these words deal with some amount or number. But percentage is actually a value out of 100. It is like asking how much/many is the ratio of cats to dogs. So it is better to use ' what percentage' instead of using either of those two words.
It is what I want to know. Today I spoke out it without any thinking. I think I learned to use "what" when using "percent", not "how many". Thank you for your teaching, Enoon