Migrate from Application Insights to OpenTelemetry

[liliankasem]

Purpose

• Migrate the sample from the Application Insights worker SDK to the OpenTelemetry approach for telemetry. Telemetry still flows to Application Insights via the Azure Monitor OpenTelemetry exporter.
• Mirrors the template change in Azure/azure-functions-templates@1cc8df7.

Does this introduce a breaking change?

[ ] Yes
[x] No

Pull Request Type

[ ] Bugfix
[ ] Feature
[ ] Code style update (formatting, local variables)
[x] Refactoring (no functional changes, no api changes)
[ ] Documentation content changes
[ ] Other... Please describe:

What to Check

• csproj: removed Microsoft.ApplicationInsights.WorkerService and Microsoft.Azure.Functions.Worker.ApplicationInsights; added Microsoft.Azure.Functions.Worker.OpenTelemetry, OpenTelemetry.Extensions.Hosting, and Azure.Monitor.OpenTelemetry.Exporter.
• Program.cs: replaced AddApplicationInsightsTelemetryWorkerService / ConfigureFunctionsApplicationInsights with AddOpenTelemetry().UseFunctionsWorkerDefaults().UseAzureMonitorExporter().
• host.json: added "telemetryMode": "OpenTelemetry".
• After deploying, telemetry continues to appear in the linked Application Insights resource.