Yes, I am aware that Qt and GTK are different stories although some compatibility when it comes to theming is possible. And Emacs is supposed to launch without having any problems under a QT or GTK oriented desktop; or even a window manager. Actually, I am running Emacs in Manjaro Sway without any problems (Sway with a bit of GTK biased setup).
I also need to reiterate that other KDE based distros such as Kubuntu, Opensuse KDE, or even Fedora KDE have no issues with installing and running Emacs. So, it has to be something to do with Manjaro KDE Edition.
I have used Manjaro KDE as it comes with the Pinebook Pro laptop I purchased. Emacs was the first application that I have tried. I installed from the “Official Repositories” and it didn’t launch. Then, I tried launching from the Konsole, it gave me a one line error. I do not remember the error exactly but it was saying something to do with colors or whatever. Googling the one line error lead me to some links about Emacs would refuse to launch when there are inconsistencies in theming. Since Manjaro KDE is using an intense mix of themes, (breeze, breath, matcha and whatever else) it made sense to me. I tried to choose one theme instead of the mixed themes but I didn’t seem to get a long way. That would include changing the GTK settings from the KDE Settings.
I am curious to learn, how did you install Manjaro and had no problems when the default Manjaro KDE images I used gave me this problem? Installing and setting up GNU Emacs was supposed to be one of the most straightforward tasks to do, esp. when it comes to installing from a Linux distro; yet, I ended up spending good time and scratching my head with what I faced with. Just to let you know, I tried official Manjaro KDE 20.04 through 20.08. I automatically assumed Emacs will be neglected in forthcoming Manjaro KDE releases, which is at 20.10 now.
Sorry, when I was saying KDE dictating I was particularly mentioning Manjaro KDE. It gave me the impression that it is designed with the assumption that users would only use what it comes with default applications or that users would like to stay with QT/Kde applications only. Now, I am thinking that perhaps the programs in its official repositories are not well tested to run with what is available in Manjaro KDE edition images.
Please let me know how you installed Manjaro and Emacs. I might consider retrying again if how you do it makes sense to me…