Finally found the issue! When I used PowerBI-CLI the problem became a bit clearer. Apparently I needed to grant access to a specific IP Address to the relevant SQL database. After that I could finally Patch the Gateway and now I can see data in my report.
We definitely need more/the same feedback in the PowerBI API SDK!
This was my error:
[ powerbi ] {"error":{"code":"DM_GWPipeline_Gateway_DataSourceAccessError","pbi.error":{"code":"DM_GWPipeline_Gateway_DataSourceAccessError","parameters":{},"details":[{"code":"DM_ErrorDetailNameCode_UnderlyingErrorCode","detail":{"type":1,"value":"-2146232060"}},{"code":"DM_ErrorDetailNameCode_UnderlyingErrorMessage","detail":{"type":1,"value":"Cannot open server 'engiep-dev-weeu-sql' requested by the login. Client with IP address 'xx.xx.xx.213' is not allowed to access the server. To enable access, use the Windows Azure Management Portal or run sp_set_firewall_rule on the master database to create a firewall rule for this IP address or address range. It may take up to five minutes for this change to take effect."}},{"code":"DM_ErrorDetailNameCode_UnderlyingHResult","detail":{"type":1,"value":"-2146232060"}},{"code":"DM_ErrorDetailNameCode_UnderlyingNativeErrorCode","detail":{"type":1,"value":"40615"}}]}}}