Like personally, had I been in your position, I would have done it like this (and I believe this would have resulted in a more peaceful interaction, but this is all theoretical):

“Hey, I saw your profile picture on Guilded. From what I remember, the person in the profile picture was Asian. I’m not sure if Asian people are considered people of color, so I wanted to ask if this was you or if this was you saying Asian people are people of color?”

And after, if they were to correct you that Asians are POC, I would have just stood corrected and moved on, less of arguing what you think it should be, what you thought it was, etc.