How do you manage a shared setup across multiple coding agents?

I'm looking for a way to manage multiple coding agents without having to maintain completely separate setups for each one. Ideally, I'd like to switch easily between Claude Code, Codex, OpenCode, GitHub Copilot, Antigravity, etc., depending on which models are best, pricing, usage limits, and so on. I'm particularly interested in having a single source of truth for things like AGENTS.md, skills, MCP servers, hooks, and other shared configurations, both globally and per project. Ideally, it should also sync across multiple machines and environments (Windows, WSL (ubuntu)). I realize some agent-specific settings and permissions probably need to be managed separately, potentially through something like chezmoi, since their setup are very different from coding agents to coding agents. Has anyone built a setup like this? Are there any good open-source tools for managing it all centrally, or is a custom dotfiles repo with symlinks/scripts still the way to go?