Yeeeeah, I feel like Otto would encourage Peter to give Harry the whole story once he figures out what all the drama's about! Honestly, he kinda thinks that confrontation went better than it really did in his world? All he knows is that Harry and Peter were close, and they must have reached enough of an understanding for Harry to help Peter find Otto, so he just kinda assumes they worked it out? So hey, why can't these two do that as well?

But even if he thinks that's the best thing to do, he won't out Peter himself. He's already pretty committed to having the back of literally any Spider-man.