I went ahead and set this up on my localhost with those permalinks and masonry, and I’m not experiencing the same issue.
So we need to figure out the difference between our installations.
Can you try #1 on this page?: https://generatepress.com/knowledgebase/debugging/
Basically, the more button grabs posts from the next page and displays them without reloading – for some reason the URLs are being changed during that process on your site.