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/settings.json

@@ -1 +1,23 @@
-{}
+{
+  "[javascript]": {
+    "editor.defaultFormatter": "biomejs.biome"
+  },
+  "[javascriptreact]": {
+    "editor.defaultFormatter": "biomejs.biome"
+  },
+  "[typescript]": {
+    "editor.defaultFormatter": "biomejs.biome"
+  },
+  "[typescriptreact]": {
+    "editor.defaultFormatter": "biomejs.biome"
+  },
+  "[json]": {
+    "editor.defaultFormatter": "biomejs.biome"
+  },
+  "[jsonc]": {
+    "editor.defaultFormatter": "biomejs.biome"
+  },
+  "editor.codeActionsOnSave": {
+    "source.organizeImports.biome": "explicit"
+  }
+}