Isn't that just true for email in general? That the most loving and attuned person sounds flat on email, at least most of the time. I think expecting email to bring emotional satisfaction in a consistent way with someone who is great with words orally in person may not be realistic.

But you're not wrong to "want affection." Why not ask in session or raise the issue about how you can get this need met the next time? Maybe there is a way she can respond on email, and you can tell her what this is, or maybe you can increase getting your affection needs in session so you don't need them between session.

I sincerely doubts she hates you. Consider the possibility that as much as she would have liked to give you something more warm or personable, perhaps that was the best she could do at the time and the place. Maybe she just didn't know how to respond in the way that would help you best. People sometimes say things like "well she could have said something really simple, like x y z" but haven't you ever failed someone who needed your support even when you were trying to show up for them? I have-- as the parent of a teenager, I've had lots of practice, especially when he and I have been physically separated or right after something distressing happens and he is at school, for example. I send what I think is a supportive, nonblaming, positive message and he thinks it's just boilerplate (rote) sympathy and I'm really criticizing him or blaming him. I look sideways at the words and can't get his reaction. Later when we talk in person it is SO much easier, he gets me and I get him and we have very few misunderstandings in person.

I also don't think you need to take on any guilt. You didn't know she was going to be away, but if the content of your email was insulting or mean and you wish you had chosen your words more carefully, a simple apology will do. For people who are trying to help me, I try to be less critical of their help than asking them to help me figure out what might work better the next time.