The EU is not (yet) a "state" in that sense and doesn't (yet) coordinate foreign policy for the member-states. Kosovo HAS been recognized by 22 out of 27 individual EU members. It's a little disturbing that the US can first recognize Kosovo and now claim that it's not a "big issue" that Serbia won't. Essentially, Biden is saying that Kosovo is a sovereign state, but that it's a-ok that Serbia maintains their territorial claim on the region (and, presumbly, act to re-take it).
Also, if Biden thinks this is not a big issue in Europe and for the EU, he's sadly ignorant of how sticky and loaded the Balkans are in Europe and how much history is connected with this region. I wish he'd pick up a history-book and look up "World War I". Then he can come back and say that instability on the Balkans is nothing to worry about...