Bug 459625

SUMMARY
On Ubuntu-based distros with the Mate or Cinnamon desktop, the deb version of Kate 21.12.3 or later does not use the system gtk theme, unless the user changes the system theme in their desktop settings while Kate is open.  No such issue is present with Kate 19.12.3 from the Ubuntu 20.04 repository.

This issue 
When I open the Deb version of Kate on an Ubuntu-based system using either Mate or Cinnamon as a desktop, the desktop's theme is not applied.  However, if I open the desktop's settings and change the theme while Kate is open, the new theme is applied to Kate, and I can get the theme I want by changing back to my original theme.  However, if I close Kate and reopen it, then the system theme will once again not be applied to Kate.

I have reproduced this issue with:
Ubuntu Mate 22.10 alpha with Kate 22.08.1
Ubuntu Mate 22.04 LTS with Kate 21.12.3
Linux Mint Cinnamon 21 with Kate 21.12.3
Linux Mint Mate 21 with Kate 21.12.3
Linux Mint Cinnamon 21 with Kate 22.04.3 from the Kubuntu Backports PPA.

On the other hand, this issue does NOT reproduce on Mint 20.3 with 19.12.3, so there has been a regression on theming.

STEPS TO REPRODUCE
1. Install Kate from the Ubuntu repository
2. Change the system theme in Mate or Cinnamon's settings to a dark theme
3. Launch Kate

OBSERVED RESULT
Desktop theme is not applied, unless you change the system theme while Kate is open.

EXPECTED RESULT
The desktop theme is automatically applied.

SOFTWARE/OS VERSIONS
Mint 21 Cinnamon, Mint 21 Mate, Ubuntu Mate 22.04, Ubuntu Mate 22.10 Alpha
KDE Frameworks Version: 5.92.0 and 5.98.0
Qt Version: 5.15.3 and 5.15.6

ADDITIONAL INFORMATION
I consider having apps "look native" to be a minor issue.  However, I consider apps having a working dark mode to be very important, because my vision impairment makes it hard for me to look at a computer screen with a light background.  With the flatpak version of Kate, I can set settings->Window Color Scheme->Breeze Dark to get a dark mode independent of the desktop theme, making this a minor issue.  However, the deb and snap versions do not seem to have this option (even on 22.08, settings->Window Color Scheme has only the option 'default').  Hence, I can't get the deb version of Kate to stay in dark mode at all.  

I also tried to test this issue with the Kate Snap and the Kate flatpak from the KDE nightly repository.  However, no QT-based flatpak apps are able to use Cinnamon's desktop themes at all, and as far as I know they've never been able to, see:
https://github.com/linuxmint/cinnamon/issues/10744
The Kate Snap also doesn't seem to use the system theme (but I haven't extensively tried to see if there is a way to make it work).