This is true for lists in Python. `a = a + b` creates a new list, but `a += b` works in-place:

    >>> a = [1, 2]
    >>> b = a
    >>> a = a + [3]
    >>> print(a, b)
    [1, 2, 3] [1, 2]

    >>> a = [1, 2]
    >>> b = a
    >>> a += [3]
    >>> print(a, b)
    [1, 2, 3] [1, 2, 3]

Concatenation is not addition in my opinion

I've often wanted something like bits++bits concatenation to work in the same way for numbers as for strings

For python, syntactically it is. In a general sense, an operation is what you define it to be. Just my opinion.

x+=y is equivalent to x.append(y)

x = x + y creates a new list, then assign it to x (highly inefficient in a loop)