You could use software to search your disk for deleted files, and recover them.
I think there are some GUID elements to these files, so simply copying them back may not work, but what you could do is create a new profile, then copy paste some of the contents of the restored file in to the new one.
If you search the forums there should be some posted examples of what the content of those files look like. A lot of it will have the same structure, but with a wrapper that has the unique stuff. You would just need to copy in the “inner” part of the XML file where the actual bindings are located, a transplant, in essence.
Mine is now working
I unplugged the usb and started flight simulator, I went into controller settings and then plugged in the usb port of the HOTAS. It said new device recognized, I selected “Default” and it showed up and is now working.
I just exited the game and went back in and it is not recognized again.
I then unplugged it restarted and then plugged it back in at the controls menu and it was working again, this time added a button by changing the filter to ALL and saved a custom profile for it and now it works through a restart.