"He is not busy today. He is relaxed."
I agree, if a period is used, they should accept two sentences. 他今天不忙。他很轻松
This 轻松 thing is yanking my chain. It doesn't make sense to say “他轻松”, yet you're giving that as a base to translate from. While there is not direct way to pick on this sentence, it is misleading and frustrating.