I have tested with a vanilla browser install to confirm this is not a plugin or theme error. The computer has been restarted into a new session.
The update today to version 71.0.3770.148 has left the browser in a sorry state. I can browse the web but I'm not able to click 'Menu' (nothing happens) or use the mouse' right-click button to open the context menu. Shortcuts work and I can access settings through the browser address bar i.e. by entering the local URL of various Opera settings pages.
I can drag pages to the bookmarks bar but dragging a page over a folder in the bookmarks bar does not trigger the folder to open to allow the page to be stored in bookmark bar folders.
The Opera Forums login button does not operate when clicked. I had to select the password field and press Return/Enter to trigger the sign in form to post.
My OS is Kubuntu 19.10 with Plasma 5.18.3.
Opera worked fine until today's update. Google Chrome (also up to date) does not have this problem.