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`

tsconfig.json

@@ -0,0 +1,45 @@
+{
+	// Visit https://aka.ms/tsconfig to read more about this file
+	"compilerOptions": {
+		// File Layout
+		// "rootDir": "./src",
+		// "outDir": "./dist",
+
+		// Environment Settings
+		// See also https://aka.ms/tsconfig/module
+		"module": "nodenext",
+		"target": "esnext",
+		"types": [],
+		// For nodejs:
+		// "lib": ["esnext"],
+		// "types": ["node"],
+		// and npm install -D @types/node
+
+		// Other Outputs
+		"sourceMap": true,
+		"declaration": true,
+		"declarationMap": true,
+
+		// Stricter Typechecking Options
+		"noUncheckedIndexedAccess": true,
+		"exactOptionalPropertyTypes": true,
+
+		// Style Options
+		// "noImplicitReturns": true,
+		// "noImplicitOverride": true,
+		// "noUnusedLocals": true,
+		// "noUnusedParameters": true,
+		// "noFallthroughCasesInSwitch": true,
+		// "noPropertyAccessFromIndexSignature": true,
+
+		// Recommended Options
+		"strict": true,
+		"jsx": "react-jsx",
+		"verbatimModuleSyntax": true,
+		"isolatedModules": true,
+		"noUncheckedSideEffectImports": true,
+		"moduleDetection": "force",
+		"skipLibCheck": true,
+		"ignoreDeprecations": "6.0"
+	}
+}