@ludivine as there are no options other than adding ecosia to the search engine list within the browser, the only thing i can suggest is to use this opera add-on which allows you to set a custom new page. Simply put the ecosia url there and whenever you open a new tab, it will open with ecosia.
I know this is not what you really ask for, but atm it's better than nothing i presume.
The submission is bullshit. I was denied submission because allegedly my extension was only pointing to a website (lets ignore the fact you can't create a login for it because it's using special client side encryption -> ProtonMail). Also lets ignore the fact it was designed to always open new tab no matter what page you had open, it would open a new tab and load the login form for ProtonMail. And final nail in the coffin that pissed me off is the fact that people have such extensions on fucking Opera Addons page that literally just load a webpage, but mine was denied because "reasons". And all this time no one gave ANY frigging reply for weeks. I was just waiting like retard until I got pissed off and started demanding answers and then someone arrogantly said it was denied because it's "just a link". Bullshit. Now I have to host the damn thing on my site and I basically stopped using it because I use it as a bookmark now and have to always specifically open an empty tab for it. Anyway, rant off, I'm surprised Opera Addons page isn't more dead given how shitty their support and submission process is.
Wrong forum, moved to the add-ons forum. But if you're talking about hosting it yourself, that is probably not allowed - for security reasons the browser will only download extensions from Opera's add-ons site.
If it's avaiable for chrome, you can add it to Opera using this extension: Install Chrome Extensions. Also I see that it requires a desktop/pc version as well, make sure you have the program installed on your machine. That could be another reason why Chrome opened when you tried to add it.