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You can get to it wherever you want. Copilot CLI is pretty great: https://github.com/features/copilot/cli

There's support in VS Code and Jetbrains IDEs. You can access your agent sessions on the web.

(I work at GitHub, but not on Copilot)

Doesn't lock you out at all. Codex already had a companion app for mobile so you can send prompts to your desktop app while you go about your business. The infrastructure is there. Server might move from your desktop to cloud at some point but not much changes. Still needs somewhere to run.

I think their goal is to lock you into their ecosystem instead of using your IDE

They want all your data. A browser doesn't get them that as well.

Codex App can spawn/control Codex agents running in the cloud.

But now is now, and what you are talking about is a future that may or may not exist.

The desktop app can become a client for their remote cloud agent solution (yuck).