chore: gateway add otel sdk

[martinothamar]

Description

OTel SDK to gateway

Verification

• Related issues are connected (if applicable)
• Your code builds clean without any errors or warnings
• Manual testing done (required)
• Relevant automated test added (if you find this hard, leave it and we'll help out)

Summary by CodeRabbit

• Chores
  • Enabled OpenTelemetry observability infrastructure for distributed tracing, metrics collection, and structured logging.
  • Integrated automatic instrumentation for ASP.NET Core and HTTP request tracking.
  • Configured telemetry exporter endpoint and service identification for observability platform integration.
  • Added exception recording to trace instrumentation for improved diagnostics.

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📝 Walkthrough

Walkthrough

This pull request integrates OpenTelemetry observability support into StudioGateway API by adding NuGet package dependencies, creating an extension method for configuring tracing, metrics, and logging instrumentation, and setting up OTLP exporter configuration through environment variables.

Changes

Cohort / File(s)	Summary
Package Management src/Runtime/StudioGateway/Directory.Packages.props, src/Runtime/StudioGateway/src/StudioGateway.Api/StudioGateway.Api.csproj	Declares and references five OpenTelemetry NuGet packages (v1.15.0) for OTLP export, hosting integration, and instrumentation of ASP.NET Core, HTTP, and runtime components.
Configuration & Infrastructure src/Runtime/StudioGateway/infra/kustomize/base/deployment.yaml	Adds two environment variables to configure OpenTelemetry: service name ("gateway") and OTLP exporter endpoint (otel-router in runtime-obs namespace).
Application Code src/Runtime/StudioGateway/src/StudioGateway.Api/Hosting/OpenTelemetryExtensions.cs, src/Runtime/StudioGateway/src/StudioGateway.Api/Program.cs	Introduces new extension method for configuring OpenTelemetry instrumentation across tracing, metrics, and logging with exception recording enabled; integrates extension into application startup.

Estimated code review effort

🎯 2 (Simple) | ⏱️ ~10 minutes

Poem

🐰 Observability hops forth today,
With telemetry traces lighting the way,
Metrics and logs now dance in the night,
OTLP exports glowing so bright!
The gateway watches with eyes open wide,
Nothing shall hide from our observant pride! ✨

🚥 Pre-merge checks | ✅ 1 | ❌ 1

❌ Failed checks (1 inconclusive)

Check name	Status	Explanation	Resolution
Description check	❓ Inconclusive	The description is minimal but matches the template structure; however, the 'Description' section lacks sufficient detail about what was changed and why.	Expand the description section to explain what OpenTelemetry components were added, their purpose, and any configuration details for better clarity.

✅ Passed checks (1 passed)

Check name	Status	Explanation
Title check	✅ Passed	The title 'chore: gateway add otel sdk' directly relates to the main change, which adds OpenTelemetry SDK packages and configuration to the gateway service.

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✨ Finishing touches

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Post copyable unit tests in a comment
• Commit unit tests in branch chore/gateway-otel-sdk

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