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

vitest.config.ts

@@ -1,9 +1,9 @@
-import { defineConfig } from 'vitest/config';
+import { defineConfig } from "vitest/config";
 
 export default defineConfig({
   test: {
     globals: true,
-    environment: 'node',
-    include: ['src/**/*.test.ts'],
+    environment: "node",
+    include: ["src/**/*.test.ts"],
   },
 });