fix(server): attach raw Error to res.err and avoid pino err key collision

Extract attachErrorContext helper to DRY up the error handler, attach the
original Error object to res.err so pino can serialize stack traces, and
rename the log context key from err to errorContext so it doesn't clash
with pino's built-in err serializer.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

server/src/middleware/logger.ts

@@ -62,7 +62,7 @@ export const httpLogger = pinoHttp({
       const ctx = (res as any).__errorContext;
       if (ctx) {
         return {
-          err: ctx.error,
+          errorContext: ctx.error,
           reqBody: ctx.reqBody,
           reqParams: ctx.reqParams,
           reqQuery: ctx.reqQuery,