The warning about the cookie you see on the console, I get the exact same thing too, and it should not cause an issue.
The failure of
GET https://sonarcloud.io/api/projects/search_my_projects?ps=500 401 is the behavior when you are not logged in on SonarCloud. If you are in fact logged in on sonarcloud.io, then this request should work. (Can you open this link in your browser? https://sonarcloud.io/api/projects/search_my_projects)
Have you followed the steps exactly as I asked you? The order of the steps is important. Make sure you are already logged into sonarcloud.io, with the correct Bitbucket account, before going to the repository settings page on Bitbucket. Please confirm!
Browser plugins such as adblock or ghostery are known to interfere with the integration sometimes, so make sure they are disabled while debugging this, to avoid unnecessary complications.
We don’t have dedicated paid support, this thread is the way!