Refactor frontend API client into focused modules

[ichwars]

Summary

• preserve api/client.ts as the public compatibility facade
• split transport, domain types, API methods, and specialized clients into focused modules
• remove the 8,156-line source-budget exception
• verify parity for all 388 public exports and 592 api methods

Local verification

• npm run build
• npm run lint
• npm run test:run (244 files, 2,848 tests)
• python tools/check_source_size_budget.py
• pytest backend/tests/unit/test_source_size_budget.py (14 tests)