Application Insights SDK integration

[troyscott]

Description

Integrate the OpenTelemetry-based Azure Monitor SDK into the FastAPI app.

Features

• Request tracing (all HTTP requests logged)
• Dependency tracking (SQL queries, HTTP calls)
• Custom metrics and events
• Correlation IDs for distributed tracing
• HTMX request tracking (custom telemetry for partial responses)

Acceptance criteria

• azure-monitor-opentelemetry package integrated
• Requests and dependencies auto-tracked
• Custom HTMX middleware logs partial vs full-page requests
• Works with App Insights resource from Application Insights provisioning #8