In the Cinnamon theme settings, I changed the “controls” theme to Adwaita-dark, and the “icons” theme to Adwaita (Adwaita-dark is not presented as on option). There doesn’t appear to be any Adwaita option for the “windows borders” or “desktop” theme.
I also installed the Adwaita-dark theme from Flathub.
It didn’t make a difference, I get the same error.
I also tried installing Mint Mate in a virtual machine to see if this issue reproduced, and it didn’t: KDE flatpak apps could launch even with org.kde.PlatformTheme.QGnomePlatform installed (although they didn’t use the Mint Dark theme). So whatever is causing the apps to not launch is present in Mint Cinnamon but not Mint Mate.