Difference in Docker Socket Behavior When Forwarding via TCP vs HTTP with HAProxy

I am looking for a service that forwards a Docker socket to TCP. So far, I have found this project and the socat project.

Here are the commands I am using:

docker run -d \
  --name docker-socket-proxy \
  -p 2377:2375 \
  -e AUTH=1 \
  -e SECRETS=1 \
  -e POST=1 \
  -e BUILD=1 \
  -e COMMIT=1 \
  -e CONFIGS=1 \
  -e CONTAINERS=1 \
  -e ALLOW_START=1 \
  -e ALLOW_STOP=1 \
  -e ALLOW_RESTARTS=1 \
  -e DISTRIBUTION=1 \
  -e EXEC=1 \
  -e GRPC=1 \
  -e IMAGES=1 \
  -e INFO=1 \
  -e NETWORKS=1 \
  -e NODES=1 \
  -e PLUGINS=1 \
  -e SERVICES=1 \
  -e SESSION=1 \
  -e SWARM=1 \
  -e SYSTEM=1 \
  -e TASKS=1 \
  -e VOLUMES=1 \
  -e DISABLE_IPV6=1 \
  -v /var/run/docker.sock:/var/run/docker.sock \
  ghcr.io/tecnativa/docker-socket-proxy:latest

docker run -d --name=dockersock2tcp -p 2375:2375 -v /var/run/docker.sock:/var/run/docker.sock alpine/socat TCP-LISTEN:2375,reuseaddr,keepalive,fork UNIX-CONNECT:/var/run/docker.sock

I noticed that using the same command can produce different results:

env DOCKER_HOST=tcp://localhost:2375 docker buildx ls

After investigating, I found that the difference is due to haproxy.cfg using mode http. When I switched it to mode tcp, it worked as expected.

Is this known behavior? Could you please explain why this option causes different Docker behavior?

Start with haproxy.cfg and compare its mode http and mode tcp settings against the Docker buildx ls commands in the report. Reproduce both forwarding paths, then determine whether the difference is expected and document the cause or the required configuration change.