You are a wonder!

I've added this little bit which, if I'm doing this right, grabs the public key direct from Hive for this account and compares it to the one returned from the Keychain response in the client.

    acc = Account(acc_name)
    match = False
    for key in acc['posting']['key_auths']:
        match = match or ans['publicKey'] in key
    if match:
        print('Matches public key from Hive')

And here's the full script.

import json
from beemgraphenebase.account import PublicKey
from beemgraphenebase.ecdsasig import verify_message
from binascii import hexlify, unhexlify
from beem.account import Account


ans = {'data':{'key': 'posting','message': '{"signed_message":{"type":"login","address":"brianoflondon","page":"http://127.0.0.1:5000/podcaster/login"},"timestamp":1613710433}', 'method': 'Posting', 'request_id': 3, 'type': 'signBuffer', 'username': 'brianoflondon'}, 'error': None, 'message': 'Message signed succesfully.', 'publicKey': 'STM7B1eanwUQhXa8tdabTi2RxHnXWtyMBd6iJDZ3Z2QA6rKHQY2WJ', 'request_id': 3, 'result': '2031e828c6673b945a14489e23a90d5502238d56fb4df568e6ab88af703a9e3bba14ea410bed5afcb42b3d164c976a49645ee2848a8b65fbd9cc77cbc574ae2ffd', 'success': True}
ansfail = {'data':{'key': 'posting','message': '{"signed_message":{"type":"login","address":"brianoflondon","page":"http://127.0.0.1:5000/podcaster/login"},"timestamp":1613710433}', 'method': 'Posting', 'request_id': 3, 'type': 'signBuffer', 'username': 'brianoflondon'}, 'error': None, 'message': 'Message signed succesfully.', 'publicKey': 'STM7B1eanwUQhXa8tdabTi2RxHnXWtyMBd6iJDZ3Z2QA6rKHQY2WJ', 'request_id': 3, 'result': '2031e828c6673b945a14489e23a90d5502238d56fb4df568e6ab88af703a9e3bba14ea410bed5afcb42b3d164c976a49645ee2848a8b65fbd9cc77cbc574ae2ffe', 'success': True}

# with open("msg.txt") as f:
#     msg = json.loads(f.read())

acc_name = ans['data']['username']
pubkey = PublicKey(ans['publicKey'])
enc_msg = ans['data']['message']
signature = ans['result']

msgkey = verify_message(enc_msg, unhexlify(signature))
pk = PublicKey(hexlify(msgkey).decode("ascii"))
if str(pk) == str(pubkey):
    print("SUCCESS: signature matches given pubkey")
    acc = Account(acc_name)
    match = False
    for key in acc['posting']['key_auths']:
        match = match or ans['publicKey'] in key
    if match:
        print('Matches public key from Hive')

else:
    print("ERROR: message was signed with a different key")