The reason is most likely a new cross-origin check: https://gitlab.com/gitlab-org/omnibus-gitlab/issues/1966
Fixed it by adding headers to the nginx forwarding:
location /api/v3/users/websocket {
proxy_pass http://127.0.0.1:8065;
(...)
proxy_set_header Host (your host name);
proxy_set_header X-Forwarded-For $remote_addr;
}