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Have you enabled the Cloud SQL api for your project? Some of the google services must be enabled first. This is done in the google cloud console. 

Thanks <@UDEJ1F5SQ>! This was my first attempt after reading the message, but it did not change anything. I enabled SQL API and the SQL Admin API (just to be sure).

Are you able to manually create a database in the console?

Just checked, `$ gcloud sql instances create test-db
 --database-version MYSQL_5_7 --storage-size=100` succeeds and I can see the DB in the GCloud UI.

I suspect some kind of (project) misconfiguration which tends to get badly reported by the Google APIs.

Found the culprit: `masterInstanceName` seems to need a special format (maybe sth. like `project/&lt;project-id&gt;/&lt;name&gt;`? Pure speculation) Removing it resulted in a working DB :man-facepalming:
Thanks <@UDEJ1F5SQ> for your time!

Oh, interesting. That's an unfortunate response from the Google API - not particularly helpful.