NameError: name 'List' is not defined

To be able to annotate what types your list should accept, you need to use typing.List

from typing import List

So did you import List?

Update

If you're using Python > 3.9, see @Adam.Er8's answer

Since Python 3.9, you can use built-in collection types (such as list) as generic types, instead of importing the corresponding capitalized types from typing.
This is thanks to PEP 585

So in Python 3.9 or newer, you could actually write:

def totalFruit(self, tree: list[int]) -> int: # Note list instead of List
    pass

without having to import anything.

To be able to specify a list of str's in a type hint, you can use the typing package, and from typing import List (capitalized, not to be confused with the built-in list)