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

eslint.config.mjs

@@ -0,0 +1,22 @@
+import js from "@eslint/js";
+import tseslint from "typescript-eslint";
+import astro from "eslint-plugin-astro";
+import globals from "globals";
+
+export default [
+  { ignores: ["dist/**", ".astro/**", "node_modules/**", "src/env.d.ts"] },
+  js.configs.recommended,
+  ...tseslint.configs.recommended,
+  ...astro.configs.recommended,
+  {
+    files: ["public/sw.js"],
+    languageOptions: {
+      globals: {
+        ...globals.serviceworker,
+      },
+    },
+    rules: {
+      "@typescript-eslint/no-unused-vars": "off",
+    },
+  },
+];