I'm gonna be real: You want kubernetes + gitops (either fluxcd or argocd or the rancher one).
I mean sure, jenkins works, but nothing is going to be as smooth as kubernetes. I originally attempted to use ansible as many people suggested, but I got frustrated becuase it struggled to manage state in a truly declarative way (e.g. when I would change the ports in the ansible files the podman containers wouldn't update, I had to add tasks for destroying and recreating the containers).
I eventually just switched to kubernetes + fluxcd. I push to the git repo. The state of the kubernetes cluster changes according. Beautiful. Simple. Encrypted secrets via sops. It supports the helm package manager as well. Complex af to set up though. But it's a huge time saver in the long run, which is why so many companies use it.