It seems they're going to fix it (finally, after only 3 years or so?) with the latest version.
I found the info in this thread: https://answers.microsoft.com/en-us/windows/forum/all/icons-in-taskbar-went-transparent-after-switching/c8258025-1818-4de5-92f4-a9394b67062c?page=1
I enrolled to the Windows Insider Programme (you can find it under Windows Update or just search directly for Windows Insider within the Windows search bar), and chose to install the latest version from the Beta Channel. You can either do that or wait until they push it out to everyone on stable release. (There's also the option to "unenroll" from those beta or DEV releases when it gets released to the general public, which I did since I prefer to have a stable build, except when the stable build is an MS joke ;-)).
It's a bit early still, but so far it seems it got rid of the issue with the icons disappearing from the taskbar when switching between virtual desktops. Fingers crossed. My build is 26120.3073.