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>

Makefile

@@ -8,11 +8,11 @@ help: ## Show this help
 dev: ## Start development infrastructure (Redis etc.)
 	docker compose -f infra/compose/shared.yml up -d
 
-lint: ## Run ESLint across the repo
-	eslint . --no-error-on-unmatched-pattern
+lint: ## Run Biome linter
+	biome lint .
 
-format: ## Format code with Prettier
-	prettier --write "**/*.{ts,tsx,js,jsx,json,md,yaml,yml}"
+format: ## Format code with Biome
+	biome format --write .
 
 clean: ## Clean build artifacts
 	rm -rf apps/*/dist apps/*/.next apps/*/target 2>/dev/null || true