After trying to connect directly to wss://api.chatengine.io/person_v4/?session_token=st-7b6efb7e-b283-4337-a5f2-a1ab9b471ee0 using https://www.piesocket.com/websocket-tester it failed once with the exact error you provided, then connected successfully three times on two consecutive attempts.

Do try again.

I wanted to suggest contacting support with chatengine.io being a private service, however from the last page of the Terms & Conditions, the e-mail address listed there points to a suspended Squarespace account so might not work.

So the next suggestion is to find a better (actively maintained) service.