Where multiple app services send their telemetry to a single application insights instance, allow configuration of alerts at the app level.
At the moment app insights alerts such a server exceptions do not differentiate which app service threw the exception if there are multiple app services talking to the same instance.
Using the existing features of Azure Monitor, you should be able to create log based alerts https://azure.microsoft.com/en-us/blog/log-alerts-for-application-insights-preview/ , which should help in this scenario. Certainly Application Map https://docs.microsoft.com/en-us/azure/azure-monitor/app/app-map is something can be used to better understand the full application topology across multiple levels of related application components and investigate failures. However the recommendation is for any independently deployable component to send telemetry to its own AI resource. Hope the information helps, feel free to revert back with your feedback if the existing features in the product are not supporting your scenario.