Well, well, well, here is a screencast video. Note that Windows did not capture the "file save" dialog when exporting, and the "Open file" dialog when importing. Don't know how to do this with built-in recorder.
The video is here https://dev.reitcoach.ch/tmp/
I first exported the page called "Kundenformular allgemein", of which the ID is 8. Next, I opened the page in the editor, and was looking for an "Import" option, but there is none. So, I closed the page again, and added a new page. On that empty new page, I chose "Import layout", and select the previously exported json file. I then closed the editor (save and close). The new page has got a new ID, namely 43.
What I wanted is a way to "import layout" into the already existing page with ID 8. I would wexpect that either in the ... menu on the page overview (where the "export" function is), Or in the page editor in the ... menu besides the "Save & Close", etc. The import should ask for confirmation, then delete all current content, and reload everything from the export json file. This will keep the ID unchanged, and all links to it will still work.