feat: API caching stats, analytics, integrations & test suite

[nottherealalanturing]

Closes #426, closes #427, closes #428, closes #429

Changes

#428 - API Caching

• CacheHeadersInterceptor — sets Cache-Control and X-Cache-Time headers
• GET /cache/stats — returns hit/miss metrics (admin only)
• DELETE /cache/clear — clears cache + resets metrics (admin only)

#429 - API Analytics

• AnalyticsService — in-memory request tracking (endpoint, method, status, response time)
• AnalyticsInterceptor — auto-records every request
• GET /analytics — top endpoints, error breakdown, avg response time (admin only)
• DELETE /analytics/reset — resets data (admin only)

#427 - Third-Party Integrations

• IntegrationsService — MLS search/listing, payment process/refund, CRM contact CRUD stubs
• IntegrationsController — REST endpoints under /integrations (JWT protected)

#426 - API Test Suite

• Endpoint tests for AppController
• Integration test for AnalyticsInterceptor
• Performance tests (1k records < 50ms)
• Unit tests for CacheStatsController, CacheHeadersInterceptor, AnalyticsService, IntegrationsService

Result: 6 suites, 37 tests, all passing ✅

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