We have a Azure based system which is growing in complexity, and we need to monitor chains of events and ensure they arrive where we expect them to arrive.
We have a on-prem Java application, which sends events to an IoT Hub. The IoT hub routes to service bus queues. We have functions that update a cosmos database, trigger other functions or route to additional queues. Some functions are also callable through an API Management instance.
Our functions are already connected to Application Insights, and here the Application Insights instance is named the same as the Function App (IIRC this naming was suggested through the form that created the AI resource)
The application map in Application Insights make me lean toward one AI per environment, to have a complete map of the system. Log Analytics also seems logical to use one per environment to be able to potentially correlate data if needed.
What is the correct path for Log Analytics and Application Insights, respectively?
If it is not as clear-cut as stated in my title, what factors do I need to consider when I start to use these services?
The correct number of instances is the one that works best for you, whether that exactly follows recommended practices or not.
The recommendation is to use one workspace per environment and make sure the cloud_RoleName in App Insights to distinguish parts of the system. Log Analytics has similar considerations.
Functions defaults to spinning up an App Insights instance along with the app because if you don't use App Insights you loose most of the logging ability- it's important to connect it to App Insights, but overriding the default behavior and connecting to a centralized workspace is common in larger systems.
There are certainly reasons you might want to split the workspaces, and you can union data across workspaces as needed to pull data together from both Log Analytics and App Insights instances.