Hello,

I experiences this behavior after Odoo 16 ugrade, because I did not yet configure the /websocket location (I still had obsolete /longpolling nginx configuration). 

After updating the configuration according to https://www.odoo.com/documentation/16.0/administration/install/deploy.html it worked like charm.

location /websocket {
    proxy_pass http://odoochat;
    proxy_set_header Upgrade $http_upgrade;
    proxy_set_header Connection $connection_upgrade;
    proxy_set_header X-Forwarded-Host $host;
    proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
    proxy_set_header X-Forwarded-Proto $scheme;
    proxy_set_header X-Real-IP $remote_addr;
  }