Hi Jens,
Unfortunately, it’s not possible. One SonarCloud organization is either bound to a BitBucket team or a GitHub org, to provide the best integration depending on the dev platform (allowing PR decoration, with GitHub you can synchronize your members for ex.).
To bind your GitHub organization, you will have to connect on SonarCloud with your GitHub account, and not with your BitBucket account. SonarCloud will find directly your GH org and projects that you can bind to SonarCloud.
However, could you explain what is your use case exactly, what is sharing between GitHub and BitbucketCloud? That would help us to see if there’s anything we can improve.
Hope it helps,
Cheers