I’ve been using chezmoi to manage dot files, that should be enough to handle AI config too. It’s easier to just have one tool do all of that.

For simple config files like AGENTS.md/skills that is true. But some configs like MCPs/Permissions/Rules require transformations per tool. On lnai's per-tool docs pages (e.g. https://lnai.sh/tools/codex/) I have documented what transforms are needed per-tool. There are quite a few of them.