At the moment only Windows handles that use case perfectly, not even macOS. Wayland comes second if the optional fractional scaling is implemented by the toolkit and the compositor. I am skeptical of the Linux desktop ecosystem to do correct thing there though. Both server-side decorations and fractional scaling being optional (i.e. requires runtime opt-in from compositor and the toolkit) are missteps for a desktop protocol. Both missing features are directly attributable to GNOME and their chokehold of GTK and other core libraries.
I hadn't heard of WSLg, vcxsrv was the best I could do for free.
Every GUI application on Windows runs an infinite event loop. In that loop you handle messages like [WM_INPUT](https://learn.microsoft.com/en-us/windows/win32/inputdev/wm-...). With Windows 8, Microsoft added a new message type: [WM_DPICHANGED](https://learn.microsoft.com/en-us/windows/win32/hidpi/wm-dpi...). To not break the existing applications with an unknown message, Windows requires the applications to opt-in. The application needs to report its DPI awareness using the function [SetProcessDpiAwareness](https://learn.microsoft.com/en-us/windows/win32/api/shellsca...). The setting of the DPI awareness state can also be done by attaching an XML manifest file to the .exe file.
With the message Windows not only provides the exact DPI to render the Window contents for the display but also the size of the window rectangle for the perfect pixel alignment and to prevent weird behavior while switching displays. After receiving the DPI, it is up to application to draw things at that DPI however it desires. The OS has no direct access to dictate how it is drawn but it does provide lots of helper libraries and functions for font rendering and for classic Windows UI elements.
If the application is using a Microsoft-implemented .NET UX library (WinForms, WPF or UWP), Microsoft has already implemented the redrawing functions. You only need to include manifest file into the .exe resources.
After all of this implementation, why does one get blurry apps? Because those applications don't opt in to handle WM_DPICHANGED. So, the only option that's left for Windows is to let the application to draw itself at the default DPI and then stretch its image. Windows will map the input messages to the default DPI pixel positions.
Microsoft does provide a half way between a fully DPI aware app and an unaware app, if the app uses the old Windows resource files to store the UI in the .exe resources. Since those apps are guaranteed to use Windows standard UI elements, Windows can intercept the drawing functions and at least draw the standard controls with the correct DPI. That's called "system aware". Since it is intercepting the application's way of drawing, it may result in weird UI bugs though.
I have a mixed DPI setup and Windows falls flat (on latest Win 11), the jank when you move a application from one monitor to another as it tells the application to redraw is horrible, and even then it sometimes fails and I end up with a cut oversized application or the app crashes.
Where as on GNOME Wayland I can resize an application to cover all my monitors and it 'just works' in making them it the same physical size on all even when one monitor is 4K and the others 1440p. There's no jank, no redraw. Yes, there's sometimes artifacting from it downscaling as the app targets the highest DPI and gets downsized by the compositor, but that's okay to me.
Windows still breaks in several situations like different size and density monitors, but it's generally good enough.
Recent Gnome on Wayland does about as well as Windows.
And, of course, doing it "wrongly" as per what OS X and Gnome does works a lot better in practice.
However, there is no common way of handling different custom DPIs / scaling in the core Wayland protocol. Fractional scaling is implemented optionally by the client and the server and both need to opt-in.