Rsync or scp from/to a Docker containerized shell

I want users can access via ssh to a container. Or, more precisely: host users can access to a containerized shell. This could look strange, but it works:

$ cat /etc/passwd | grep staging

staging:x:1001:1001::/home/staging:/usr/local/bin/stagingclish

$ groups staging

staging : staging docker

$ cat /usr/local/bin/stagingclish 

#!/bin/sh
cd /home/cloud/docker/myproject-staging && docker-compose run --rm --entrypoint=bash php-cli $@

php-cli is just a custom build from php:7.4-cli image, including some utilities like rsync. Also, /etc/passwd is mounted from host.

I can login with ssh staging@myhost.

I can invoke commands:

ssh staging@myhost ls /

Creating myproject-staging_php-cli_run ... 
Creating myproject-staging_php-cli_run ... done
CHANGELOG.md
COPYING.txt
Gruntfile.js.sample
...

Now I would like be able to use scp and rsync commands to retrieve/upload files from/to the container.

But:

scp staging@myhost:/var/www/repo/auth.json.sample .

Creating myproject-staging_php-cli_run ... 
Creating myproject-staging_php-cli_run ... done
usage: scp [-346BCpqrv] [-c cipher] [-F ssh_config] [-i identity_file]
           [-l limit] [-o ssh_option] [-P port] [-S program] source ... target
1

And

rsync staging@myhost:/var/www/repo/auth.json.sample .

[... rsync help ...]

rsync error: syntax or usage error (code 1) at main.c(1580) [client=3.1.3]
1
rsync: connection unexpectedly closed (0 bytes received so far) [Receiver]
rsync error: error in rsync protocol data stream (code 12) at io.c(228) [Receiver=3.2.3]

I don't even know if this is possible. Could anyone bring some light?