That's kind of weird. The swipe to close gesture is not an app feature. It's system gesture and sould work on all apps. That said, I do have a few apps that take two swipes, as if there is something else they want to do. They just bounce a bit on the first swipe, but then the the bar appears at the bottom and the second swipe does the trick.
I don't have FaceBook, so I can't check it out.
Another way to close apps (if you have Stage Manager or Windowed apps on) is to make a short swipe from the top of the screen. The new menu bar should show. Then you can choose File and Close Window. Still a bit awkward without a mouse, but less finicky than the small colored dots.
Even more obscure, but a possible last resort, you can tell Siri to "Go to the Home Screen"
Even more, more obscure, there is a Go to HomeScreen action in the Shortcuts. You could create this shortcut and add it to the Control center. You would need to go to Settings as Control Screen and turn on Enable in Apps for this to work.
It's also possible to get back to the HomeScreen using the Assistive Touch feature in Accesibilty.
I realize than most likely none of these tips help, but I after I went though all the ways I know of to get back to the HomeScreen, I couldn't help but write them down.