If so, click the "X" and it won't show up again (unless Opera has issues saving the root/browser/default_browser_infobar_last_declined value in the "Preferences" file in the profile folder).

At the URL opera://settings/defaultBrowser, you'll see there's no option not to check for the default browser. There's no option anywhere else in the settings UI. You just have that bar and the X on it to say "don't bug me again".

If so, try searching for default in the settings page and you should see the option to set Opera as the default browser.

@xaunloc In Settings there is an option to check if Opera is the default browser, just turn that off.

This might seem like a silly question, but exactly where is the magical option?

I ask, because that was my first thought. I looked for any such option, I didn't find it and perhaps more disturbingly Opera itself could not find it when I used Opera's own Settings Search to look for any setting including the word default

So, whatever Opera calls this magical setting, apparently its name does not mention the word "default"

There is a setting option to MAKE Opera the default browser, but neither I not Opera itself have been able to find any setting that controls whether or not Opera checks to see if it is the default browser.