OK, actually the game generally freezes after alt+tabing out and back in. All you can see afterwards is black screen and a white cursor. But the game needs to tab out to save, so...

Running Win11.

Exact same problem here. I can alt tab normally and get the game back up. But when I do the load thing and it opens the explorer window to save in. It alt tabs and won't go back into the game. Same with loading.

I think I have found a workaround. You need to use DXWnd application to launch War Wind. I will attach configuration of it, that I'm using myself and it is working on Windows 11 (most of the time). Remember, that for it to work, you need to delete or rename the ddraw.dll file from game main directory!
The problem with this solution is, that you will not see any kind of cut scenes/cinematics, but you can play them in any media player (they are in War Wind\Data\VIDS\).

This will allow you to run the game, but yoy may get crashes on save/load game from time to time. To mitigate it, try to not click too fast through game menus (yes, it sound silly, but it seems to work). If the game crashes, wait few seconds and start it anew (closing DXWnd application, if needed). If that will also cause problems, try open the Task Manager and on Process tab, find all War Wind processes and kill them, as they may cause problems.

To avoid irritation, try to save often, it will help progress the game if it will crash.

PS. You may want to run DXWnd (or GoG Galaxy client, if you set DXWnd in its custom executables) in Administrator mode, as it seems to increase the stability.