API search user by user field?

I have a custom user_field where my Discourse users have my website IDs. I use this field to show link like “Go to profile on main website” in the forum profile, but I’d also like to search by this ID. Please note, I’m not looking for search from user perspective, but from admin perspective, I have admin-API token.

Seems like API provides only way to look-up either by username (which would work for me if not tremendous restrictions like “cannot start with minus”, “cannot have emojis and other proper unicode” etc…) or by Discourse ID or by some “external id”. The latter seems to be the most relevant, but as I understood, I cannot just fill it with my random data, I need some SSO logic which I don’t have.

So, question - how can I search Discourse users with admin API token with something else except Username? Both email and user field would make my life way better than it is now, when I try to look for username, but sometimes I can find nothing, so I have no connection…