does extension have functional button (next to address bar)?
if not, you won't see it in Opera, but you will in Chrome
This is something that was changed recently in Chrome
All extensions are listed on toolbar, and then it's up to users to hide those extensions inside hamburger menu or not.
This creates many confusions and problems, for instance with pageAction icons (those that were inside address bar), because in this case, they are always visible or always hidden, and that breaks functionality
Luckily, Opera didn't implement that.
So, maybe your extension doesn't have (functional) toolbar icon at all, or maybe it is designed to be pageAction (and you see it in Chrome all the time)
.... or maybe that extension is specifically designed for Chrome, usually extensions from Google developers linked to some of the Google services
can you link (or name it) that non-working extension so that we can test it?
