Unfortunately, it seems the Opera team aren't interested in giving us an option for Ecosia as the default search, so the only solution for now is to switch, Brave Privacy Browser includes Ecosia as one of the default search options on install, so you can use Ecosia search out of the box.

I just installed Opera for mobile on my phone for the first time.
I currently have Chrome, Edge and Brave installed.
When starting the Opera browser I had no prompts for importing data (open tabs, bookmarks, passwords) from my other browsers, and I don't see that option in the settings menu.

Can anyone suggest how to do it?

Unfortunately, it seems the Opera team aren't interested in giving us an option for Ecosia as the default search, so the only solution for now is to switch, Brave Privacy Browser includes Ecosia as one of the default search options on install, so you can use Ecosia search out of the box.