brotherofurs
Welcome back. First of all you should know he may be a Rabbi but he is human and most likely even if he has worked on many of his flaws he still has many he may not be aware of so dont expect perfection or even near perfection, especially if we are talking about a Rabbi who is young or relatively so.
Another thing, most Rabbis today are busier today than Rabbonim of yesteryear because now they get called, emailed, texted and people also call them at home and expect them to be always on call. I know of Rabbonim that get texted serious Shaylos. On a regular basis. So please dont be quick to judge this Rabbi. He may have been expecting an important text or he always must check every text that comes in as it comes in to make sure its not an emergency.
As a further point, I think your friend has to realize that while she may have been feeling like she was saying something very important and personal, she may not have disclosed that to the Rabbi before he picked up his phone. As you yourself said “and was ready to disclose a serious problem,” “The situation was so hard for her at home that she was ready to cry.” You expect him to read minds too?!