Base64Encoder class wrapper
You've got a class with only two classmethods and one staticmethod. One classmethod does not use the class argument, the other one refers to a static method. Hence none of the class' methods use either the class or one of its instances. Thus, you do not require a class at all:

def encode_basic(usr, pwd):
    token = base64_encode(f"{usr}:{pwd}")
    return f'Basic {token}'

def encode_bearer(token):
    return f'Bearer {token}'

def base64_encode(token):
    return b64encode(token.encode('ascii')).decode('ascii')


Also consider adding docstrings to the functions, that explain how they are supposed to be used. Without knowlege of your program's context it is hard to tell, why the strings are being formatted in the respective ways and why one string needs ASCII encoding.