@burnout426 Unfortunately, the reinstallation steps didn't help. Opera updated itself again and set itself as the default browser.
It looks like this is done not by the installation itself, but by Opera when you run it the first time after it updates. When I ran Opera after the latest update, I got multiple Windows prompts telling me that Opera wants to make changes to my device. I allowed the changes and then checked 'Default Apps' in Windows and confirmed that Opera became the default browser again.