When you click See Price on an unpublished (draft) copy of a property page, it opens your live property page and does not show a quote. This is expected behavior while the page is a draft.
Why this happens. The See Price button sends the visitor to the property’s web address with the check-in and check-out dates added to the URL. When External Property Pages is enabled, that address is your own live property page. From a draft copy, the button lands on the live page, which does not yet have the HomeRunner booking box and ignores the dates in the URL.
What you can do. Publish the new version at the same URL as the existing live page by keeping the same slug. Once it is published, the button reloads the same page with the dates in the URL, and the HomeRunner booking box shows the nightly rate, the total before tax, and the Instant Booking button.
Keeping the existing URL also matters because search results and map pins point to that address.