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`

.gitignore

@@ -136,3 +136,6 @@ dist
 .yarn/install-state.gz
 .pnp.*
 
+# AI agents
+.opencode
+PLAN.md