feat(api): add Context Management API and routes

- Introduced a new `context` module and its endpoints for Context Management.
- Added `/context` route to the API router for assembling LLM context, token counting, budget management, and cache invalidation.
- Implemented health checks, context assembly, token counting, and caching operations in the Context Management Engine.
- Included schemas for request/response models and tightened error handling for context-related operations.

backend/app/api/main.py

@@ -5,6 +5,7 @@ from app.api.routes import (
     agent_types,
     agents,
     auth,
+    context,
     events,
     issues,
     mcp,
@@ -35,6 +36,9 @@ api_router.include_router(events.router, tags=["Events"])
 # MCP (Model Context Protocol) router
 api_router.include_router(mcp.router, prefix="/mcp", tags=["MCP"])
 
+# Context Management Engine router
+api_router.include_router(context.router, prefix="/context", tags=["Context"])
+
 # Syndarix domain routers
 api_router.include_router(projects.router, prefix="/projects", tags=["Projects"])
 api_router.include_router(