How can I list, show all the charts installed by helm on a K8s?
helm list --all-namespaces
Where does helm keep the which repository installed etc?
By default in Secret objects in the same namespace as the release, but this can be changed.
Can I somehow export the helm’s repository list and history
Not really. You can use helm get values to get the set of values a particular release was installed with. I don’t believe there’s an option to tell you where the chart originally came from.
Rather than trying to export this information from a cluster, a better approach is to make sure you have a copy of the information you need to recreate it in source control. If the cluster state is small enough, you can try recreating it on a desktop-based Kubernetes installation (Docker Desktop, minikube, kind) for test purposes. This could be a directory of shell scripts with install commands and matching value YAML files; there are also higher-level tools like Helmsman and Helmfile that try to maintain an installation of several charts together.