[FEATURE] Desktop Code tab: project file-tree explorer pane (like VS Code's Explorer)

Problem Statement

The desktop app's Code tab has panes for chat, diff, browser, terminal, file, plan, tasks, and subagent — but no way to browse the working directory. The file pane only opens a single file after clicking a path in chat, and the diff pane lists only changed files. To see the project's actual folder structure, I have to leave the app ("Continue in IDE" or a terminal tree), which defeats working in a single window.

Proposed Solution

Add a "Files" pane to the existing pane system (Views menu + shortcut): a read-only-first tree of the session's working directory, where clicking a file opens it in the existing file pane, with the current right-click affordances (Open in editor, Show in Finder, Copy path). Files changed in the session could carry the same modified-dot indicators the diff pane uses.

Alternatives considered

"Continue in IDE" works but forces a second app for what is often just orientation ("what did Claude create where?"). #38439 asked for this in Cowork and was closed as stale/not planned; this request is specifically for the Code tab, where the pane infrastructure already exists.