chore: migrate from ESLint/Prettier to Biome

- Add biome.json with recommended preset + custom rules
- Remove eslint.config.mjs (root, apps/react, apps/elysia)
- Remove .prettierrc and .prettierignore
- Update package.json: remove eslint/prettier deps, add biome scripts
- Update Makefile: lint/format targets to biome
- Update CI (lint.yml): eslint -> biome ci
- Update VSCode config: biomejs.biome extension + default formatter
- Apply biome format --write to all files
- Update submodule pointers for react and elysia

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

.vscode/extensions.json

@@ -1,8 +1,7 @@
 {
   "recommendations": [
     "nrwl.angular-console",
-    "esbenp.prettier-vscode",
-    "dbaeumer.vscode-eslint",
+    "biomejs.biome",
     "ms-playwright.playwright",
     "firsttris.vscode-jest-runner"
   ]