Codex UI shows git branch but not the effective working directory used by agent tool calls

Title:
Codex UI shows git branch but not the effective working directory used by agent tool calls

Issue:
The Codex UI exposes the current git branch, but it does not clearly show the effective working directory/repo root being used by the agent for each turn or tool call.

Why this matters:
The visible terminal prompt can remain on one directory while the agent executes commands with an explicit different workdir. In that case, Ctrl-J or the terminal prompt can show:
C:\Users\Richard\source\repos\PhxBiz\Eventryx\Eventryx.AgenticSDKPlugin

while the agent is actually editing/running commands in:
C:\Users\Richard\source\repos\PhxBiz\phoenix-sdk-integration-mcp

This creates confusion and risk because branch information is only meaningful relative to a repo/worktree. A user may believe work is happening in one repo when files are actually being created or modified in another.

Expected behavior:
Codex should show the effective working directory and git repo root alongside the branch. Ideally it should distinguish:

• Thread default CWD
• Visible terminal prompt CWD
• Last tool-call workdir
• Git repo root
• Current branch

Suggested UI:
Active workdir:
<absolute path>

Git repo:
<absolute repo root>

Branch:
<branch name>

Last command workdir:
<absolute path>

Impact:
This would reduce wrong-repo confusion, improve trust in multi-repo workflows, and make worktree changes easier for users to audit.