I agree with all the comments here saying "stick with Win32" --- this is "a mess" that you can easily avoid.

Speaking as a long-time Win32 programmer, the requirements for your app are doable in a few KB (yes, kilobytes --- my vague estimate is less than 8KB) standalone executable. This is how I arrived at that:

Enumerating the machine’s displays and their bounds

A few API calls. Probably a few hundred bytes.

Placing borderless, titlebar-less, non-activating black windows

Creating non-functional windows is trivial. Another few hundred bytes at most.

Intercepting a global keyboard shortcut

A few dozen bytes to call SetWindowsHookEx.

Optionally running at startup

Write to the appropriate registry key. A few hundred bytes.

Storing some persistent settings

Ditto. Another few hundred bytes. You can use a .ini file too, for around the same size.

Displaying a tray icon with a few menu items

Most of this size of this will be the icon itself - a few kilobytes; the next biggest contributor will be text strings; and the rest is accomplished with a few hundred bytes of API calls.

Add another few hundred bytes of (not much) logic, round up to a kilobyte and add maybe another for general overhead.

But, in 2026, writing a greenfield application in a memory-unsafe language like C++ is a crime.

Don't be swayed by the propaganda. Especially if your application has essentially no untrusted input.

How do you make your win32 app look good to the average person?

If you don't want to spend quite so much time byte shaving, and you don't want to deal with memory safety or _UNICODE, you can do it in .Net Framework in half the time.

IDK man, I wonder how TF did the creators of Winamp do it? Were they so much smarter than the programers of today? And Winamp 2.95 still works on WIndows 11 today.