Yes, if they detect you to be using multiple websites to bypass a maximum bet amount limit set by them they would more than likely limit you across all the websites that they operate. You can confirm this with Betby themselves.

Think of it like casino is just being rented by bookmaker to place their sportsbook, Casino itself is just using 3rd party services for their sportsbook category which means you are limited by the bookmaker whatever casino you are using as long as it’s same bookmaker.

If you read the statement of BC carefully, they have no control over bookmaker decision since they are just using their service. Most likely you will always be limited as long as you play on same bookmaker. The case of the OP is just different because they are trying to void the bet that already have a result few days ago.