Finally i was able to let this infrastructure works, but there are some considerations:

1. i've created a service principal from app registration "appr-func-test-01"
2. i've added the service principal to database admin AAD group as the managed identity func-test-01
3. most important: you need to stop and restart the function app. For what i've understood, when the azure function try to connect to the database with the manageg identity, it asks for a token. This token remains valid (or invalid) till next ask so if at the time of request the azure function was not able to connect, it remains unable unless you allow it and restart the function app.