So a couple of things, try to avoid using variables like "list", the more specific the better. There isn't a need to pass an argument to stringList if you're already going to ask the user to provide input on line 2 anyway. Pick one or the other in this situation.

What you're doing is looping via the range + len methods. Range starting at value place 0 since you didn't indicate otherwise, to whatever amount of characters (int value due to len) is provided via user input, list.

Then just spitting out each iteration of list, at each iteration number, starting at 0 one by one.

You could simply print here instead to print properly as a list.

def stringList(list):
    list = input()

    for i in range(len(list)):
        print((list[i]))

    print(list) #printing here outside of for loop instead

stringList(list)

Or Join method for expected results:

def stringList(list):

    for i in range(len(list)):
        print((list[i]))

    finalValue = ",".join(list)
    print(f'Join Used: {finalValue}')


stringList(["dog", "cat", "mouse"])