Answering by point.
1. Upgrade Desktop to the latest version: 2.52.4921.682 (November 2017). --> I have already the latest version, I have the 64bit installed
2. Check your BigQuery settings. starry-braid-156516 could be project id. --> I know that starry-braid-156516 is a project id but as you can see I am trying to connect to a public dataset, and the project id is bigquery-public-data.... Moreover, in the list of my projects, I do not have any starry-braid-156516 project...
3. Connect to BigQuery using a user with the owner Privilege. --> The owner privilege where? On the BigQuery project? I am trying to connect to a public dataset, I can not be owner of that project! If I try to connect to one of my private projects where I am owner, Power BI tries to connect to starry-braid project the same way....