Hey @aneta-s
When you say Google is displaying the correct site, you mean in the search results it displays text from the old site, or do you mean Google Chrome?
If different devices are displaying different content (or different browsers on the same device), it is highly possibly the old content is cached on the device. Clearing the device/browser cache, hard refreshing, etc. should help remedy this.
It would also help if you could provide screenshots of the content you should see versus the content you are seeing. (For what it is worth, I see the same content on desktop and mobile.)
Failing this, a request ID for content that is incorrect will help Netlify determine if there is any possibility of a cache issue on the CDN.