Definitely the last post from my side about this matter. It's an issue caused by syncing options. So it may be related to a "My Flow" connection that didn't work or being logged out from your Opera account.
For me, logging in again didn't solve this problem though. But by accident I found a solution that has worked for me so far on different machines, either with Windows or Mac:
Just deinstall Opera and make sure you keep your personal browser data and not erase it! Then just reinstall Opera again. And by whatever way there you'll see the dissappeared favicons in the address bar again.
It's a workaround as it shouldn't happen at all. But so far this has brought it all back. Good luck with it!