Is it possible to create an OS that simply automatically runs .exe files through WINE/Proton/Bottles?
Zorin already does that out-of-the-box. See: https://help.zorin.com/docs/apps-games/windows-app-support/#run-apps-in-exe-and-msi-files
And if you want to take it to the next level, there's ReactOS, which is basically an opensource reverse-engineered Windows - but sadly it's development is slow and it's hardware support is extremely lacking. But it exists, and does qualify as an answer to your question. For all practical purposes though, Zorin is what you're looking for.
Sounds like what you're after is lxqt-panel. Problem is, it's not quite ready yet - things like positioning settings, taskbar and a few other plugins do not work, last I checked, but feel free to check it out.
Presently, the main issue is that Qt's layer-shell-qt isn't complete yet - without layer-shell support, certain key taskbar-y things wouldn't work, such as listing and management of active windows, menu popups, reserving the screen space etc. But I suspect it's inching pretty close to completion with the looming release of KDE 6.
For now, check out this page and keep an eye for updates to it: https://github.com/stefonarch/LXQt-Wayland-files/blob/main/lxqt-panel.md
In saying that, what's your issue exactly with Waybar? I use it on Wayfire and it works fine, and the taskbar plugin does display icons for Qt based apps.