To speak truly, more than a few students who are native English speakers walk roughshod across English verb tenses. Your "I've been working all day" is what I would say, too. Usually I would say that at a time when, having begun work early in the morning, I am still working when I'm prompted by circumstance to speak. The present perfect tense expresses this situation, ah..., perfectly.
If one of my students made either of the first two statements, and if I were inclined to play the gruff, grammar-growling curmudgeon, I would reply with something to the effect of "So, does that mean that you are no longer working?" Simple past and past progressive tenses imply with varying degrees of certainty that the action described happened in the past, but is no longer happening.
Hence, "I worked all day today" suggests that the sun has dropped below the horizon and that it's time for everyone to have a root beer.
Meanwhile, "I was working today" suggests that work took place for a period of time, but has now concluded. Let's have some more root beer.
As I say, many children born and raised in the lap of the English mother tongue pay no heed to this issue. Those non-native speakers who try so carefully to sort it out deserve good wishes and support.