feat: Implement Phase 1 API layer (Issues #28-32)

Complete REST API endpoints for all Syndarix core entities:

Projects (8 endpoints):
- CRUD operations with owner-based access control
- Lifecycle management (pause/resume)
- Slug-based retrieval

Agent Types (6 endpoints):
- CRUD operations with superuser-only writes
- Search and filtering support
- Instance count tracking

Agent Instances (10 endpoints):
- Spawn/list/update/terminate operations
- Status lifecycle with transition validation
- Pause/resume functionality
- Individual and project-wide metrics

Issues (8 endpoints):
- CRUD with comprehensive filtering
- Agent/human assignment
- External tracker sync trigger
- Statistics aggregation

Sprints (10 endpoints):
- CRUD with lifecycle enforcement
- Start/complete transitions
- Issue management
- Velocity metrics

All endpoints include:
- Rate limiting via slowapi
- Project ownership authorization
- Proper error handling with custom exceptions
- Comprehensive logging

Phase 1 API Layer: 100% complete
Phase 1 Overall: ~88% (frontend blocked by design approvals)

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

backend/app/api/main.py

@@ -2,12 +2,17 @@ from fastapi import APIRouter
 
 from app.api.routes import (
     admin,
+    agent_types,
+    agents,
     auth,
     events,
+    issues,
     oauth,
     oauth_provider,
     organizations,
+    projects,
     sessions,
+    sprints,
     users,
 )
 
@@ -25,3 +30,19 @@ api_router.include_router(
 )
 # SSE events router - no prefix, routes define full paths
 api_router.include_router(events.router, tags=["Events"])
+
+# Syndarix domain routers
+api_router.include_router(
+    projects.router, prefix="/projects", tags=["Projects"]
+)
+api_router.include_router(
+    agent_types.router, prefix="/agent-types", tags=["Agent Types"]
+)
+# Issues router - routes include /projects/{project_id}/issues paths
+api_router.include_router(issues.router, tags=["Issues"])
+# Agents router - routes include /projects/{project_id}/agents paths
+api_router.include_router(agents.router, tags=["Agents"])
+# Sprints router - routes need prefix as they use /projects/{project_id}/sprints paths
+api_router.include_router(
+    sprints.router, prefix="/projects/{project_id}/sprints", tags=["Sprints"]
+)