Is the site newly added to Google? Google takes a few days to get your favicon. Also: How did you implement the favicon, is it a static one or a dynamic one?

yes, it's new to google

i created all dimensions of favicon in public folder
favicon.ico
favicon-32x32.png
etc

then setted up a sitemap.ts and robots.ts

and inside

app/layout.tsx

i added this code

export const metadata: Metadata= {
  title: "Ayla Holiday Homes",
  description: "Find your perfect stay",
  icons: {
    icon: [
      { url: '/favicon.ico', sizes: 'any' },
      { url: '/favicon-16x16.png', type: 'image/png', sizes: '16x16' },
      { url: '/favicon-32x32.png', type: 'image/png', sizes: '32x32' },
    ],
    apple: [
      { url: '/apple-touch-icon.png', sizes: '180x180', type: 'image/png' },
    ],
    shortcut: '/favicon.ico',
  },
  manifest: '/site.webmanifest',
  other: {
    'msapplication-TileColor': '#000000',
    'msapplication-config': '/browserconfig.xml',
  },
}; 

Yeah then google will take some time to do it. I also have a new site which I added 3 days ago to google and there is still no favicon too.

So these meta tags appear in the sites live html if you inspect?

You can also test if you setuped the favicons correctly: https://realfavicongenerator.net/favicon-checker