Multi-root support for Codex

### Feature Description:

Follow up to #17262. In that PR, Codex and Claude were left out of the multi-root support changes since they operate more independently of our internal setup than internal agents. Claude is tracked in https://github.com/eclipse-theia/theia/issues/16334. Here, the request is to support multi-root workspaces properly for Codex.

Start by reading follow-up issue #17262 and the multi-root support changes that excluded Codex. Then trace the existing Codex integration and compare its workspace handling with the supported internal agents. Done means Codex works properly in multi-root workspaces, with behavior validated across the relevant workspace configurations.

Written by the indexing model from the issue text.