Using a single TCP connection for requests to different hosts between CF servers and origin servers

We encountered a situation where requests to different hosts(example.com, example.org) came through a single TCP connection. We use proxy servers that determine which node to forward the request to and then cease connection analysis. As a result, all requests over one TCP connection will be handled by a single node. This leads to issues as the node processing requests from the first host may not handle requests from other hosts. On the link https://developers.cloudflare.com/load-balancing/load-balancers/, there is information that you can send requests for different HTTP sessions through one TCP connection, but nothing is said about different hosts.