chore(tooling): migrate from Biome to ESLint + Prettier

Replace Biome lint/check/format scripts with ESLint and Prettier commands, add Next + TypeScript oriented ESLint flat config, and remove biome.json. Update dependencies and lockfile to a single lint stack with Prettier-based formatting.

eslint.config.mjs

@@ -0,0 +1,43 @@
+import { defineConfig, globalIgnores } from "eslint/config"
+import nextVitals from "eslint-config-next/core-web-vitals"
+import nextTypescript from "eslint-config-next/typescript"
+import prettier from "eslint-config-prettier/flat"
+
+const eslintConfig = defineConfig([
+  ...nextVitals,
+  ...nextTypescript,
+  {
+    files: ["**/*.{ts,tsx,mts,cts}"],
+    languageOptions: {
+      parserOptions: {
+        projectService: true,
+        tsconfigRootDir: import.meta.dirname,
+      },
+    },
+    rules: {
+      "react-hooks/exhaustive-deps": "error",
+      "react-hooks/set-state-in-effect": "off",
+      "react-hooks/incompatible-library": "off",
+      "@next/next/no-async-client-component": "error",
+      "@typescript-eslint/no-explicit-any": "error",
+      "@typescript-eslint/no-non-null-assertion": "error",
+      "@typescript-eslint/no-unused-vars": [
+        "warn",
+        { argsIgnorePattern: "^_", varsIgnorePattern: "^_" },
+      ],
+      "@typescript-eslint/consistent-type-imports": [
+        "error",
+        { prefer: "type-imports", fixStyle: "inline-type-imports" },
+      ],
+      "@typescript-eslint/no-floating-promises": "error",
+      "@typescript-eslint/no-misused-promises": [
+        "error",
+        { checksVoidReturn: { attributes: false } },
+      ],
+    },
+  },
+  prettier,
+  globalIgnores([".next/**", "out/**", "build/**", "node_modules/**", "next-env.d.ts"]),
+])
+
+export default eslintConfig