Bump? This issue still occurs on Opera GX build 67.0.3575.87 on Windows 10 64bit. Running a vega64, ryzen 5 2600x, 16GB of RAM and the browser is installed on an SSD. Running a dual monitor setup like the OP. This issue severely hinders my enjoyment of the browser and seeing it still occur so many months after this initial post is worrisome to say the least.
You could launch a command prompt and run:
"C:\Program Files\Opera\launcher.exe" --makedefaultbrowser
If that doesn't work, you can right-click the command prompt shortcut, run it as administrator and then do the same command.