You are not supposed to use the same instance for working and window-managing. Using a dedicated setup for EXWM and another for the rest is somewhat mandatory with this, to prevent exactly this problem.
EXWM has been my daily driver for years and I use the same Emacs for window management, email, text editing, IRC and a few other things.
This can be a problem if you choose applications (like Gnus) which are known to have slow, blocking operations but those usually have modern alternatives.
This can be a problem if you choose applications (like Gnus) which are known to have slow, blocking operations but those usually have modern alternatives.