Hi @d-ms-22 thanks for the question.
The short answer is no. Currently there is no way to use Managed Identity to access App Insights without connectionstring
According to the documentation you shared, after the Azure AD authentication is enabled, you can choose to disable local authentication. This configuration will allow you to ingest telemetry authenticated exclusively by Azure AD and impacts data access (for example, through API Keys). You can disable local authentication by using the Azure portal, Azure Policy, or programmatically. Once your resource has disabled local authentication, you'll see the corresponding info in the Overview pane but the connectionstring is still required to configure the Application Insights SDK in your .NET Core project
hope that helps.
-Grace