I know that this is an old issue but I had the same problem this year when I got my Note 20 Ultra. You simply go to settings>advanced features>floating notifications. The 3 options are off, bubbles and smart pop-up view. To be able to reply to messages and mark messages as read at the top of your screen without opening the message app and leaving your current screen is to switch it to off. Hope this helps someone else!
Also, one of my contacts weirdly had its own category in my messages settings and it's own notification settings, it was set to bubble and I couldn't change it or remove the category (which was her contact name). I even deleted the contact and the category went away, however when I put her back into my contacts, the category appeared again so I then had to open apps in my settings, find messages and clear the data. It doesn't delete texts but does reset to original settings and her category with its own special bubble setting was gone and everything's back to normal!