iOS 13 just added a delightful feature where long press on a web browser link it opens on Safari, even if you are in Firefox, and even if you are in private browsing. It pops up a split screen window that has no close-window button. The only way to close the pop up window is to exit your browser and go Home, and then go to Safari to clean up.
I too found that annoying. If I understand correctly what you’re referring to, if you notice closely, there is a “Hide Preview” on the top right of that Safari popup. Tap that once and you’ll be back to just seeing a nice menu of what to do with the link and no more opening the link in a Safari popup.