It doesn't happen when I set it back to Default [E]. And fortunately I see that the issues I mentioned back in this topic are quite solved:
https://forums.opera.com/topic/40532/speed-dial-is-the-same-across-tabs
Although when opening a new tab you could still see a flash of how the previous Speed Dial was before.

So it seems this is an issue that happens with Speed Dials except the first one (shared or not), just that if it's shared, you are always stuck to that first one and don't experience the problem.