PowerBI <> Synapse Serverless <> Azure Function app (Python)

UPDATE : hereby the less complex situation: forget the Function app.
As suggested, I followed the steps in this Microsoft tutorial : https://learn.microsoft.com/en-us/azure/synapse-analytics/sql/tutorial-connect-power-bi-desktop

> I have created a PBIx with >>> "Azure SQL DB connection" <<< using the Demo Database method
> It all works on my desktop, but when deploying it to a cloud PBI workspace, the credentials are removed.

> All 3 connection methods work on my computer : OAUTH, sql credentials & service principal.

Two remaining questions :
* how do I get it work WITHOUT editing the credentials manually afterwards (it works like that, but I do want a solution without other manual interactions) ?

* how do I get this work WHILE editing the credentials in an Azure Function app (Python) ? Please know that the type is "Sql" while I expected "AzureSQLDb"
> so as written before: THAT should be the reason of failure...