There is currently no built-in way to trigger a webhook when a mirrored repo is synced.
This is a known issue:
I would like to help fix this, either by creating a useful workaround or improving gogs itself. I have zero Go experience and my attempts at creating a fix on my own haven’t been successful. If I had a basic outline of what needed to be changed to make this work, I think I could learn enough Go to make it happen. Any help would be greatly appreciated!