Ok, so, I've had a similar / same issue. Kept getting "you're not connected to the internet, try again" thing on the YT side bar (On the site), and when I was clicking on my account icon on the right hand side.
Also, YT Music didn't work in the Opera Side bar plug in.
It is not an Opera issue. It is an YouTube issue. Basically, if you don't allow YT to show you adds and to track you via the Privacy Protection settings that are shown in the post from Noobie18, then YT will not work on your Opera Browser, because YT basically blocks you unless you allow it to track you.
Use this info at your leisure, as soon as I added Youtube to the Privacy Protection exception part, it worked.