For Microsoft.Web/connections resource type there is no assignment of managed identity. I would assume you use this resource type for Azure Logic App (Standard). In such case the managed identity is assigned to the Logic App Standard resource and when you use the connector you specify the authentication and which managed identity is used. Additionally for resource type Microsoft.Web/connections you have to specify kind to v2. Also either parameterValueType should be set to Alternative or parameterValueSet configured. You can find more information with example at ARM template for API connections and managed identities. Note that if it single-authentication or multi-authentication depends on the capabilities of the connector. You can check the capabilities by query the Rest API endpoint behind the value for managedApiId.