feat(backend): integrate Sentry SDK for production error tracking

[Nicks-19]

Description

This PR integrates the Sentry SDK into the backend FastAPI application to enable comprehensive error tracking, performance profiling, and context tagging for production environments.

Closes #531

Changes

1. Dependency updates: Added sentry-sdk>=2.0.0 to backend/requirements.txt.
2. Configuration: Added sentry_environment (defaults to ENVIRONMENT or "production") and sentry_profiles_sample_rate to the FastAPI settings in backend/app/config.py.
3. Initialization & Tags: Enhanced init_error_tracking() in backend/app/services/error_tracking.py to configure Sentry with dynamic environment and profiling options, alongside attaching metadata tags (app_name, ai_provider, ai_model, llm_enabled) and app settings context.
4. App Integration: Updated FastAPI lifespan in backend/app/main.py to run the initializer, and modified the global exception handler to automatically capture all unhandled errors via sentry_sdk.capture_exception().
5. Testing: Implemented comprehensive unit tests in backend/tests/test_error_tracking.py covering disabled states, configuration mapping, metadata tags verification, and capturing behavior in the global error handler.

Verification

• All 402 tests pass successfully.
• Verified that global exception handler captures errors using mock test clients with raise_server_exceptions=False.

[imDarshanGK]

@Nicks-19 Resolve conflicts

[Nicks-19]

Hi @imDarshanGK
I have resolved the merge conflicts in backend/requirements.txt by merging the latest changes from main and keeping the dependencies clean.

Could you please approve the CI workflows and review the PR?
Thanks!