What’s your favourite German word that has no English equivalent? Mine is ‘doch’.

We do too have an equivalent in English! ... 😉

"Too" is not one, I would argue! It's more "auch" (also in this sentence).

When said with the right intonation and emphasis, "too" in that example does do the same thing as "doch" in the German equivalent of the sentence.

Maybe :) To me, "too" is similar to an "as well" whereas "doch" has more a ring of "though" (expressing something that contrasts/contradicts what has been previously said).

Of course, when you say "X does not apply to Y", then "X applies to Y too" expresses something contrasting. But this seems to be more a "coincidence" of both sentences' semantics, rather than part of "too".