Tested on CentOS Stream 9 with Cockpit and traefik v3.
A full working Podman Quadlet example, can be seen here: https://github.com/foxws/foxws/tree/main/podman
You need to overrule the Cockpit Web Service to not use TLS.
TLS is being offered by traefik in this example:
sudo systemctl edit cockpit.serviceEnter the following to overrule:
[Service]
ExecStart=
ExecStart=/usr/libexec/cockpit-tls --no-tlsCreate /etc/cockpit/cockpit.conf:
[WebService]
Origins = https://cockpit.example.com
ProtocolHeader = X-Forwarded-Proto
ForwardedForHeader = X-Forwarded-For
AllowUnencrypted = true