A single extension that accesses both google translate and DeepL sounded good. Unfortunately I tried to follow the instructions, signed up for a free DeepL account to get the authentication key, and there is no such key. It looks like DeepL withdrew free access to the API and developed their own Firefox extension here: https://addons.mozilla.org/en-US/firefox/addon/deepl-translate/

So this Simple Translate extension and documentation is badly out of date and no longer has the functionality it claims.