chore: add ESLint + Prettier, fix all lint errors

- Install eslint, typescript-eslint, eslint-plugin-astro, prettier,
  prettier-plugin-astro, globals
- Add flat eslint.config.mjs with recommended rules for JS, TS, Astro
- Add .prettierrc with astro plugin
- Add lint, lint:fix, format, format:check scripts
- Fix prefer-const, no-unused-vars, no-useless-assignment across codebase
- Fix AdBanner.astro JSX fragment for Prettier compatibility
- Add eslint-disable around Yandex/Top.Mail.Ru inline scripts
- Auto-format entire codebase with Prettier

.prettierrc

@@ -0,0 +1,11 @@
+{
+  "plugins": ["prettier-plugin-astro"],
+  "overrides": [
+    {
+      "files": "*.astro",
+      "options": {
+        "parser": "astro"
+      }
+    }
+  ]
+}