[FEATURE] Desktop (Cowork): task panel auto-opens when the first chat message is sent; no setting to keep it closed

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

On the Claude Desktop app (Windows, Cowork tab), the right-side task panel (Progress, Working folder, Context) opens automatically the first time a message is sent in a chat - every chat, every time.

At that point the sections are empty ("Track tools and referenced files used in this task" placeholder), so the panel consumes roughly a quarter of the window width while conveying no information.

There is no setting to prevent it from auto-opening. The collapse toggle in the window header only applies to the current chat; the next chat pops the panel open again on first send. The user's preference is never remembered.

This is the same class of problem as #75523 (left sidebar pinned state: layout preference exists but is not persistent, discoverable, or configurable).

Proposed Solution

1. Do not auto-open the task panel by default, or at minimum do not open it while its sections are empty.
2. Persist the user's last open/collapsed choice across chats and app restarts.
3. Expose a setting (e.g. Settings > Appearance > Task panel: "Auto-open" / "Stay closed") so the behavior is configurable by browsing settings.

The manual show/hide toggle already exists in the header - users who want the panel can open it themselves.

Alternative Solutions

Manually collapsing the panel with the header toggle every single chat. It pops open again on the first message of the next chat, so this must be repeated constantly.

Searched Settings and the desktop docs (code.claude.com/docs/en/desktop) - no option or documented shortcut for this panel.

Priority

Medium - Would be very helpful

Feature Category

Configuration and settings

Use Case Example

1. Open the desktop app, start a new Cowork chat to ask a quick question.
2. Send the first message - the right-side task panel pops open automatically with empty Progress / Working folder / Context sections.
3. Collapse it with the header toggle.
4. Start the next chat and send a message - it pops open again.
5. Repeat for every chat, every day.

With a persisted preference, steps 3-5 disappear: the panel stays closed until deliberately opened.

Additional Context

Environment: Claude Desktop app, Cowork tab, Windows.

Related: #75523 (persistent "keep sidebar open" setting for the left sidebar) - same underlying request: layout state should be persistent and configurable, not reset per chat.