refactor(backend-core): split monolithic index.ts into 15 focused modules

Extract config, context, logger, types, db, http, overview, performance,
provider-registry, scheduler, task-dispatcher, microservice-proxy,
ssh-bridge, and egress-tcp into separate files. index.ts now only handles
server setup, HTTP/WebSocket routing, and startup orchestration.

No behavioral changes — all existing tests and health checks pass.

scripts/src/check.ts

@@ -30,7 +30,7 @@ function commandItem(name: string, command: string[]): CheckItem {
 
 function unifiedLogRotationItem(): CheckItem {
   const serviceFiles = [
-    "src/components/backend-core/src/index.ts",
+    "src/components/backend-core/src/logger.ts",
     "src/components/frontend/src/index.ts",
     "src/components/provider-gateway/src/index.ts",
     "src/components/microservices/code-queue/src/index.ts",