Python List NOT modifying in place while splicing?

I have a list of chars. I want to insert a string in between the chars at given index. For that I wrote a function to insert the item (string) in the list in-place. The list inside the function is correct BUT it is NOT modifying the original list that I am passing. I believe Python List is mutable.

def insert_inplace(lst, idx, item_to_insert):
    lst = lst[:idx] + lst[idx+1:]
            
    lst[:idx] = lst[:idx]
    lst[idx+1:] = lst[idx:]
    lst[idx] = item_to_insert
    print(lst) 
    # getting correct answer here

string_list = ["a", "b", "c", "d", "e"]
replacement = "new inserted item"
i = 2
insert_inplace(string_list, i, replacement)
# string_list is not getting modified

you're reassigning the lst variable within the function. Reassigning lst to a new list breaks the connection between the original list

def insert_inplace(lst, idx, item_to_insert):
    lst[idx:idx] = [item_to_insert]  # Insert item_to_insert at index idx
    print(lst)  # Print the modified list inside the function

string_list = ["a", "b", "c", "d", "e"]
replacement = "new inserted item"
i = 2
insert_inplace(string_list, i, replacement)
# string_list should now be modified
print(string_list)

Output

['a', 'b', 'new inserted item', 'c', 'd', 'e']

More Simpler Approach

def insert_inplace(lst, idx, item_to_insert):
    lst.insert(idx, item_to_insert)

string_list = ["a", "b", "c", "d", "e"]
replacement = "new inserted item"
i = 2
insert_inplace(string_list, i, replacement)
print(string_list)

Yeilds same

['a', 'b', 'new inserted item', 'c', 'd', 'e']

time complexity is o(n)