Show the current working directory in Claude Code conversations

When I have several Claude Code coding conversations open, often in different git worktrees of the same repo, there's no quick way to see which directory a conversation is running in. Right now I have to scroll back or ask Claude.

Request: show the session's current working directory, ideally with the git branch, somewhere always visible, such as the conversation header or the session list. It should update if the session changes directory.

Why: working in the wrong worktree risks editing or committing on the wrong branch. Remote and cloud sessions make this worse, because the directory paths are long and auto-generated.

Surfaces: web, desktop, mobile and the CLI. In the CLI, /statusline can show the directory, but the other surfaces don't seem to have an equivalent.