feat: initial project structure and generate API types

Initialized `package.json`, add tsup build config (CJS/ESM/DTS), wire up
full Makefile targets (lint/test/check/build), add missing BadRequest
response component to OpenAPI spec, generate TypeScript types from spec,
configure biome to exclude generated files, and add `@types/ws`

tsup.config.ts

@@ -0,0 +1,11 @@
+import { defineConfig } from "tsup";
+
+export default defineConfig({
+	entry: ["src/index.ts"],
+	format: ["cjs", "esm"],
+	dts: { resolve: true },
+	outDir: "dist",
+	clean: true,
+	sourcemap: true,
+	minify: false,
+});