Version of Windows (and I don't mean just "Windows 10", but which actual build) and of Opera? I have 4 versions of Opera installed (Developer, Beta, Stable and GX) and they don't fight over which is default (Developer is). Oh, also which type of install (All users, current user, or standalone)?

@technomicks Download the Opera GX 64-bit offline installer from https://www.opera.com/download. Then, close Opera.

Then, uninstall Opera (don't choose to delete your data when uninstalling).

Then, launch the Opera installer, click "options", set "install path" to "C:\Program Files\Opera GX", set "install for" to "all users", uncheck "import data from default browser", check "Make Opera the default browser", adjust any other options, and install.

Then, Opera will show up in Default Programs in Windows and you'll be able to set it as the default browser.

Only the pre-defined search engines that come with Opera can be set as the default one.

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.