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.

.prettierrc.json

@@ -0,0 +1,7 @@
+{
+  "semi": false,
+  "singleQuote": false,
+  "tabWidth": 2,
+  "printWidth": 100,
+  "trailingComma": "all"
+}