An apology that requires you to comfort the speaker has left part of the work unfinished.

Some apologies quietly reverse the roles. The person who caused the harm arrives so distressed about being someone who would do such a thing that you end up reassuring them, and by the end you have done the emotional work while they have received the relief. Nothing about your side of it has been addressed.

If this happens, you are allowed to receive the apology without managing the aftermath. A simple thank you for saying that is enough, and you can return to your own point later. When you are the one apologising, keep it short and carry your own distress elsewhere.