Best Case and Worst Case of an Algorithm: When are they considered to be the "same"?

Question

I am trying to determine the Best Case and Worst Case of the algorithm below but I have been really confused since our professor claims that the Best Case and Worse Case of the algorithm are the "Same"

    import math
    def sum(Arr, left, right):
        if(left>right):
            return 0
        elif(left == right):
            return Arr[left]
        else:
            mid = left+ math.floor((right-left)/2)
            leftSum = sum(Arr, left, mid)
            rightSum = sum(Arr, mid+1, right)
            return leftSum + rightSum;
    def findSum(Arr):
        return sum(Arr, 0, len(Arr)-1)
    
    
    arr = [1,2,3,4,5,7,8,9]
    print(findSum(arr));

The algorithm finds the sum of an array by divide-and-conquer, and here were my initial thought:

Best Case: The input array only has 1 element, hence it would meet the second condition and return Arr[left]. No recursion is involved and takes Constant Time(O(1))

Worst Case: The Input array could be arbitrary large(N elements), and each element needs to be scanned once at least, and it would take Linear Time(O(N))

I saw an explanation from another post with similar questions, and the explanation was that no matter how large/small the input array is, the algorithm has to loop over it once, so it's Linear Time for both Worse/Best Case. But I was still confused, the Best Case of the algorithm does not involve any recursion, so can we still claim that it is Linear Time(O(N)) instead of Constant Time(O(1))?