Ok I can give some additional details.
First regarding project set-up.
I am using Qt UI for dialogs and such without problems.
I added a .qrc file named QtResource.qrc to the project containing a couple of image files:

I can see that file getting rcc'ed, generating a file named qrc_QtResource.cpp, which does get compiled:
1>------ Build started: Project: DrivenController, Configuration: Debug x64 ------
1>Rcc'ing QtResource.qrc...
[...]
1>DllEntry.cpp
1>qrc_QtResource.cpp
1> Creating library C:\Users\Nicolas\source\repos\3ds max\2021\LinkController\LinkController\\obj\x64\Debug\\DrivenController.lib and object C:\Users\Nicolas\source\repos\3ds max\2021\LinkController\LinkController\\obj\x64\Debug\\DrivenController.exp
1>DrivenController.vcxproj -> C:\Program Files\Autodesk\3ds Max 2021\Plugins\DrivenController.dlc
1>C:\Users\Nicolas\source\repos\3ds max\2021\LinkController\LinkController\obj\x64\Debug\DrivenController.dlc.muiLanguage neutral file successfully created at "C:\Users\Nicolas\source\repos\3ds max\2021\LinkController\LinkController\obj\x64\Debug\DrivenController.dlc.ln".
1>MUI file successfully created at "C:\Users\Nicolas\source\repos\3ds max\2021\LinkController\LinkController\obj\x64\Debug\DrivenController.dlc.mui".
1>Done building project "DrivenController.vcxproj".
========== Rebuild All: 1 succeeded, 0 failed, 0 skipped ==========
Now regarding using the Qt resources.
If I use an absolute path on an external image file, i.e.:
QIcon mutedIcon("<absolute path>\\Images\\muted.png");
the icon will be created and show up as expected.
But if I try to read it from the resource file:
QIcon mutedIcon(":/DrivenController/Images/muted.png");
the icon is null.
I tried to list the content of the Qt file system with this code:
QDirIterator it(":", QDirIterator::Subdirectories);
while (it.hasNext()) {
qDebug() << it.next();
}
There are many entries, including max-specific content, like
":/qt-project.org/styles/commonstyle"
":/qt-project.org/styles/commonstyle/images"
":/qt-project.org/styles/commonstyle/images/networkdrive-16.png"
":/qt-project.org/styles/commonstyle/images/networkdrive-32.png"
":/qt-project.org/styles/commonstyle/images/dvd-16.png"
":/qt-project.org/styles/commonstyle/images/cdr-16.png"
":/Icons/CommandPanel"
":/Icons/CommandPanel/Utilities"
":/Icons/CommandPanel/Utilities/ConfigureButtonSets_32.png"
":/Icons/CommandPanel/Utilities/ConfigureButtonSets_20.png"
":/Icons/CommandPanel/Utilities/ConfigureButtonSets_24.png"
":/Icons/CommandPanel/Utilities/ConfigureButtonSets_16.png"
but nothing under ":/DrivenController/"
The Qt doc on using resources https://doc.qt.io/qt-5/resources.html suggests "you need to force initialization of your resources by calling Q_INIT_RESOURCE() with the base name of the .qrc file."
but calling
Q_INIT_RESOURCE(QtResource);
outside of any name space, in miscellaneous places did not make a difference.