Translation:I am busy these days.
Nothing in this sentence explicitly implies "days." 段 could refer to any duration of time and relies on context. No native Chinese speaker says "这段时间" and means being busy these days off handedly. In fact, this seems like a response to a very specific question in which the question could have been "when are you busy today?"
I agree there seems to be want of a word such as very or pretty to go with busy. It doesn't line up so well with the Chinese translation without it, and it sounds a little clunky in English. I've been quite busy these days, or I've been very busy recently seems more natural and more accurate of a translation