Copy one page from one document to another in thumbnail view in Pages

No. Apple has not re-implemented this old Pages '09 feature.

You can select the text to copy to the other document, click and hold as you drag this selection (text clipping) between the open Pages documents. Release to drop in the recipient document. Same drill using copy and paste into the recipient body text.

"I'm answering my own question: you need to export the Pages files to Pages 09. !"

A solution that will work temporarily, but that will expire when you purchase a new Mac, or when you update the Operating System on your current one.

Should that be an issue, I'd suggest using the Provide Pages Feedback menu item in the Pages menu to make a feature request, and ask for this feature to be reinstated in the current versions of Pages.

Regards,

Barry