The main reason Win32 can't handle automatic background suspension or low-power push notifications is simply that those features haven't been exposed to it. There's nothing preventing a Win32 program from receiving those types of notifications and then being force-ended by the OS if it doesn't respond in time.

When I first started porting programs to Windows ARM64, I didn't have an ARM64 device and had to test in QEMU. It ran extremely slowly, probably 1/50th of real time. All UWP programs like Calculator ran like a slug. But which programs still ran reasonably? Classic WinDbg and Task Manager. Two programs that were still plain Win32.

There are significant issues with Win32, namely its lack of a permissions and isolation and lack of hardware acceleration in the old windowing UI (User/GDI). But the idea that Win32 is inherently power inefficient is, IMO, just BS. Its roots go back to CPUs that were orders of magnitude slower than modern CPUs and there is nothing difficult about making a Win32 program that idles at 0% CPU when not in use.