Activity ID is not reliably persisted in logs

For HTTP requests, the Activity ID passed by the infrastructure (Web Apps FE) is not reliably persisted to functions logs, making HTTP flow investigations difficult as we can't easily correlate with the function executions.

Opening this to investigate and track fixes/enhancements.

This would require capturing activity IDs in the FE and trace them all the way into the FunctionsLogs to ensure they're flowing through.

We should also ensure API calls outside of a function execution context (e.g., pings, status calls) also have an activity ID captured and persisted.

Start by tracing the activity ID from the HTTP request infrastructure through the FE and into FunctionsLogs, then inspect API calls outside function execution such as pings and status calls. Done means activity IDs are captured and persisted consistently so HTTP flows can be correlated with function executions and those other API calls.

Written by the indexing model from the issue text.