feat: add ESLint with error-handling rules

Add ESLint v9.35+ with typescript-eslint recommended config and
error-handling rules: preserve-caught-error (enforces { cause } when
re-throwing), no-unused-vars with caughtErrors:all, and
eslint-plugin-no-catch-all (warns on catch blocks that don't rethrow).

Fix existing violations: add error cause to container-runtime rethrow,
prefix unused vars with underscore, remove unused imports.

https://claude.ai/code/session_01JPjzhBp9PR5LtfLWVDrYrH

src/routing.test.ts

@@ -1,6 +1,6 @@
 import { describe, it, expect, beforeEach } from 'vitest';
 
-import { _initTestDatabase, getAllChats, storeChatMetadata } from './db.js';
+import { _initTestDatabase, storeChatMetadata } from './db.js';
 import { getAvailableGroups, _setRegisteredGroups } from './index.js';
 
 beforeEach(() => {