Ehh each tool it's job. Wanted to agree but pre commit checks to keep secrets from entering the graph makes sense at every level for me. Anything that is too keep the git DB itself clean goes there. So if you have Conventional Commits standards precommit checks make sense. Checks for secrets. Tbh that's the furthest I've done for a precommit.
Pre push is a good place to start any orginzational checks though. Pipelines for tests and smell checks or anything fuzzy really (can normally be seen by maintainers in the merge requests). K8s (like fleet, argocd, etc) for ops checks (is this running, is the service accepting requests, etc).