And did you paste the content of your old profile folder into the new one?
Were sync enabled in the old Opera and is enabled in the current one?

The default fonts are the same.

Not possible as far as I know.

If you had spent some time reading the forums, you probably would find you answer at https://forums.opera.com/post/137016

Programs Files/Opera is the installation directory, no user data is stored there in a typical installation. It's valid for (almost) all programs installed on Windows.
User data is usually stored at %appdata% directory.

Backup your profile folder and paste it into the new computer.

Without a context, that video doesn't mean much. Anyway, Opera here opens kinda fast.

Maybe it's being hidden by the OS? Don't know about MacOS but Windows hides common file extensions by default.

The site is trying to make me download a swf file. The same happens in other browsers based on Chromium, maybe because I don't have Flash installed.

In Edge it ask me to allow Flash.

And what profile directory is Opera using?

For this to happen, both Opera and Ecosia need to want it, and it has to be profitable for both.
So did you already contacted Ecosia? What they say about it? Di dthey already try an agreement with Opera?