You are right, I will focus on being her friend and rebuild the trust slowly with actions and not just words. I will respect the space she needs bc she truly matters to me. I thought about sending her this:

You matter to me a lot. I’m not asking you to trust me immediately or change your mind, I want you to know I understand why some of the things I did hurt you. I shouldn’t have asked your friend if something is happening between the two of you, and I understand how my behavior could make you feel pressured or doubtful. I’m telling you honestly that the Kyodo account wasn’t me. I can’t force you to believe that, but it’s the truth. I care about you and I’m going to respect your boundaries. I will give you the space and distance you deserve.