Website translation works better when you can do it inline while you're on the page you want to translate, rather than having to go to a separate website (translate.kagi.com) to paste a link there. This way you can translate pages that don't have an easily accessible link. For example they might require login or there is some state that you can only reach by performing actions on the page.
You can look at the built in firefox local translation for inspiration. It can translate the whole page as you see it right now and also works on selection. So you can select some text and right click and select "translate this text".
There are a couple of unofficial firefox addons that integrate kagi translate. It would be better if this came officially from kagi.
See above.