For the v1 runtime, there is a nice document that describes where this is. https://github.com/Azure/azure-functions-host/wiki/Retrieving-information-about-the-currently-running-function
For the v2 runtime, there was no such luck. After looking at the environment variables and just the variables available when running the function I found it under $TriggerMetadata.InvocationId.
My own, my precious, InvocationId.
Explanation: you may need this if you want a way to tag external logging to a particular run of the Azure Function, which the InvocationId will identify for you. You can search for something like the below in logs to find relevant logs for that invocation.
traces | where customDimensions.InvocationId == "06358a22-5eae-4aaa-8742-42ea2451c2c6"
The plot thickens: apparently RandGuid is the value that does this, according to the documentation: https://docs.microsoft.com/en-us/azure/azure-functions/functions-reference-powershell#triggermetadata-parameter
BUT, InvocationID is the value that the function actually returns to the log when it finishes executing, and is the value available in logs from Application Insights, unless I am missing something. Getting clarification here and re-writing this later if needed: https://github.com/MicrosoftDocs/azure-docs/issues/43580