Is there any way to reproduce Windows' new "Sets" feature? For some time now, I have been looking for a macOS tool that allows me to group apps similar to the upcoming Sets feature in Windows 10.

So far, my search has been fruitless and I have been considering diving into app development for macOS to see if I can build it myself, but I strongly suspect that Apple does not support 'wrapping' applications like this.

Does anyone know of anything similar?
I don't think an existing utility exists that is exactly like the upcoming Sets feature in Windows 10.

On the other hand, I cannot see why you suspect that Apple does not support "wrapping" applications like that. The Sets feature sounds like a window manager. You can find examples of open source macOS window managers, and use that as a basis for creating your own that essentially does tabbed windows.

Take a look at for example chunkwm:

https://github.com/koekeishiya/chunkwm