Basically everything you need to do:

class SHA1:
    def __init__(self) -> None:
        self._message = b''

    def update(self, message: bytes) -> None:
        self._message += message

    def digest(self) -> bytes:
        """Compute hash for self._message"""

After calling the update(message) method, you update the variable inside the class. When digest() is called, you work with this previously saved variable.
I checked, scripts of multiple calls to update() are not tested. For a single instance of a class, the update() method is called once.
p.s. Judging by your code, you are on the right track.