Hi,
It’s hard to determine why it happened with that specific wallpaper since it has already passed. However, since the button is now appearing on the new wallpaper, it was likely just a temporary bug.
If you’re unable to click the button, make sure Microsoft Edge is set as your default browser and Bing is set as your default search engine. The “Like what you see?” button is tied to both Edge and Bing, so having them set as the defaults may help ensure it works properly.
As for the wallpaper, you can press Windows + R then paste this path to open the folder where Windows Spotlight assets are located:
%LocalAppData%\Packages\Microsoft.Windows.ContentDeliveryManager_cw5n1h2txyewy\LocalState\Assets
In the folder, you’ll see files with long string filenames. These are your Windows Spotlight wallpapers. You can open them by right-clicking a file, selecting Rename, and adding .png to the end of the filename to convert it into a valid image format. To sort the files by date and easily identify which one was your recent wallpapers, right-click an empty area in the folder, select View > Details, and then sort the files by date.