[ANNOUNCEMENT] Heroes 3: World Tournament - an add-on for tournament games.

I don't know about a direct connection – for example, I use a dynamic connection and play through GR. And isn't GR better at maintaining the connection? I used GR when it was impossible to play through Hamachi....

Dynamic and direct are not mutually exclusive concepts. However, gray and direct (white) are contradictory.
GR definitely doesn't affect the connection. The fact that it might be worse with Hamachi is quite possible.
What GR does: it eliminates the routine task of creating a host (clicking buttons: New Game -> Tournament -> TCP/IP -> Server -> My Game (OK)), and on the client side
(clicking buttons: New Game -> Tournament -> TCP/IP -> Search by IP - Manual IP entry of the opponent)

it seems that in case of a connection break in GR, saving is problematic...

Maybe, maybe... I haven't looked into it much, but I think if I can implement similar functionality, it won't be a problem; I can adjust it as needed.