Thanks for your feedback.
No, I am not attempting cross-subscription access. The Subscription IDs mentioned are the IDs I see on the Shared Access links, so I think this is a bug in Azure. For that, I will raise a support ticket.
About the setup we want to achieve: we found out that the issue was caused by the fact that we disable Public Access on SQL Server and we were trying to setup the datasource on the Cognitive Search resource after disabling the access. This causes an issue because we try publicly to access the SQL Server instance (using the portal). So, in the end we created a VM within the VNET and from that VM we did the whole setup and that works.
Thanks all for the answers.