Can't paste into client after installing Bottles using flatpak

On my main gaming PC I installed Bottles through AUR, and pasting into and World of Warcraft works fine.

When installing Bottles on my mini gaming PC, I decided to use Flatpak instead, since that’s the recommended method. It installed fine, but now I’m unable to paste into the client or World of Warcraft. I can copy text out, but I can’t paste text in. I’m guessing this is because of the sandboxed nature of Flatpak applications.

I’ve attempted to Google this and search these forums, but with absolutely no results.

Is copy/paste supposed to work? Does anybody have any idea why it doesn’t? Does it work for everyone else?