I have same issue since the last update of phonelink and have been using Google messages for more than 1 year with phonelink without this problem. Basically phonelink thinks my most replied sms thread is a group chat with (even though it is not in the SMS app) and if I try to reply from phonelink I get 2 sms, one to me and one to the actual receiver. I have tried to create a new sms thread from phonelink directly to see if this was a problem with the update but after a reply the same thread gets merged with the fake group thread.
My google message app for sms has not been updated in the meanwhile so this must be a problem with the recent updates in phonelink.