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/index.ts

@@ -33,7 +33,6 @@ import {
   getAllTasks,
   getMessagesSince,
   getNewMessages,
-  getRegisteredGroup,
   getRouterState,
   initDatabase,
   setRegisteredGroup,