It strikes me that I went on at great length but didn’t directly answer your main question.

Targeted emotions felt via affective empathy (at least for me and presumably for others) can be either directed at the same target as they are for the source or untargeted.

I think the way it works is that if I both feel affective empathy and experience cognitive empathy, then the emotion ends up aimed at the same target, since the cognitive empathy provides a framework for it. And that’s the way it is most of the time.

And yes - if I’m the target and I grasp the idea behind it, so experience cognitive empathy, then I do become my own target.

If I don’t have the context for cognitive empathy though, the emotion is just sort of there. I’m just aware that being in this place or around these people or whatever is putting me on edge. I don’t quite feel the full sense of the emotion then, presumably because it needs context and a target to fully manifest. Instead, I feel a vaguer, less directed form of it - like being around angry people without really focusing on it, so not getting cognitive empathy, just leaves me feeling unaccountably stressed and cranky. Or being around sad people makes me feel unaccountably melancholy.

And along with that, one thing it definitely does is prime me to find something to direct it at. It’s not just that I feel unaccountably cranky or melancholy or whatever, but that I’m likely going to (over)react to the first thing that happens that provides something like justification for the full-blown emotion. Like once it starts, it has to find a way to fully manifest.