fix(fastapi): use effective_route_context path for prefixed routers

[ericapisani]

FastAPI >= 0.137 stores the prefix-resolved path in scope["fastapi"]["effective_route_context"] instead of scope["route"].path, so transactions/segments were showing the unprefixed /users/{user_id} instead of the full /api/users/{user_id} for routers mounted with a prefix.

This fix prefers effective_route_context.path when available, falling back to route.path for older FastAPI versions.

Fixes PY-2530
Fixes #6571

[linear-code]

PY-2530

[ericapisani]

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Codecov Results 📊

✅ 90590 passed | ⏭️ 6031 skipped | Total: 96621 | Pass Rate: 93.76% | Execution Time: 320m 11s

📊 Comparison with Base Branch

Metric	Change
Total Tests	📈 +96530
Passed Tests	📈 +90505
Failed Tests	📉 -4
Skipped Tests	📈 +6029

➖ Removed Tests (4)

View removed tests

• test_transaction_no_operation_name[True-True-async_app_client_factory-True-framework_integrations0]
  • File: tests.integrations.strawberry.test_strawberry
• test_transaction_no_operation_name[True-False-async_app_client_factory-True-framework_integrations0]
  • File: tests.integrations.strawberry.test_strawberry
• test_transaction_no_operation_name[False-True-async_app_client_factory-True-framework_integrations0]
  • File: tests.integrations.strawberry.test_strawberry
• test_transaction_no_operation_name[False-False-async_app_client_factory-True-framework_integrations0]
  • File: tests.integrations.strawberry.test_strawberry

All tests are passing successfully.

✅ Patch coverage is 100.00%. Project has 2421 uncovered lines.
✅ Project coverage is 89.75%. Comparing base (base) to head (head).

Files with missing lines (1)

File	Patch %	Lines
sentry_sdk/integrations/fastapi.py	100.00%	⚠️ 1 partials

Coverage diff

@@            Coverage Diff             @@
##          main       #PR       +/-##
==========================================
+ Coverage    29.67%    89.75%   +60.08%
==========================================
  Files          192       192         —
  Lines        23615     23619        +4
  Branches      8130      8132        +2
==========================================
+ Hits          7007     21198    +14191
- Misses       16608      2421    -14187
- Partials       654      1340      +686

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