What's the difference here:
Hey, sorry, I've been so busy at work.
Hey, sorry I've been so busy at work.
Are both okay?
In the first instance, we don't specifically know what the speaker is "sorry" about. The phrase "I've been so busy at work" is an explanation/excuse relating to whatever it is that the speaker is sorry about. So the speaker may be saying "I'm sorry I haven't called you. I have been so busy at work that I haven't had time".
In the second instance, the "sorry" relates specifically and exclusively to the fact that the speaker has been so busy at work.
I'm not a teacher of English, but I have spoken it for (almost) all of my life....