Add configurable structured logging

Adds a leveled JSON logger (error/warn/info/verbose/debug, controlled via
LOG_LEVEL) wired into the Express API (access log, error middleware,
crash handlers, memory heartbeat) and the Next.js server (page-request
proxy, instrumentation crash handlers, heartbeat). LOG_LEVEL is exposed
through compose.yaml, and both services now rotate their Docker logs
(json-file, 20m x 10 files) instead of growing unbounded. Intended to
capture long-running diagnostic data for the intermittent 502s seen on
the Docker host.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

src/server/middleware/error.middleware.ts

@@ -1,12 +1,19 @@
 import type { NextFunction, Request, Response } from "express";
+import { createLogger, toErrorMeta } from "../../shared/logging/logger.js";
+
+const logger = createLogger("api");
 
 export function errorMiddleware(
   error: unknown,
-  _req: Request,
+  req: Request,
   res: Response,
   _next: NextFunction
 ) {
-  console.error(error);
+  logger.error("request handler threw", {
+    method: req.method,
+    path: req.originalUrl,
+    ...toErrorMeta(error),
+  });
   res.status(500).json({ error: "Internal Server Error" });
 }