[FEATURE] Add toggle to hide active PR card in Code session chat footer

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

Context

QA engineer using Claude Code Desktop app daily for test automation work (Katalon Studio scripts, TestRail integration). Multiple long-running sessions tied to GitHub repos with active PRs.

The Problem

When a Code session is connected to a GitHub repo with an open PR, a PR card is permanently displayed in the chat footer — directly above the message input box:

🔀 Open | #5 feat/sprint-4c-4d-cross-session-profile-edit | +5,287 -2 | CI

This card is persistent and cannot be dismissed.

<img width="881" height="139" alt="Image" src="https://github.com/user-attachments/assets/337469d8-ed5e-4a4d-9c24-99c73350163a" />

Why this is a problem

1. Always-visible UI element competing for attention with conversation content during long sessions
2. Not actionable in many workflows — many users don't manage PRs from the Desktop app; they use GitHub web UI or CLI
3. No setting exists to hide it — checked Settings panel thoroughly
4. Different from existing requests — prior issues (#34194, #39497, #18475, #31475) focused on sidebar diff stats or status footer. This is specifically about the PR summary card above the input box, which is a separate UI element

What I'd want

A simple setting under Settings > Claude Code > Display (or similar) with a toggle:

• [ ] Show active PR card in session footer

Default can stay ON to preserve current behavior for users who like it.

Who this affects

• QA / testing engineers running long debugging sessions
• Users with many active PRs across multiple branches
• Anyone who manages PRs outside the Desktop app (GitHub web UI, CLI, IDE extensions)
• Non-IDE workflows (documentation, ops, knowledge management)

Proposed Solution

Add a user setting to toggle visibility of the active PR card in the chat footer. See above for details.

Alternative Solutions

Auto-hide the card when the user starts typing, or after N seconds of inactivity. But a simple settings toggle is cleaner and more predictable.

Priority

Medium - Would be very helpful

Feature Category

Configuration and settings

Use Case Example

Every Claude Code session I open against a repo with active PRs. The card takes ~10% of vertical screen space and never goes away.

Additional Context

<img width="881" height="139" alt="Image" src="https://github.com/user-attachments/assets/337469d8-ed5e-4a4d-9c24-99c73350163a" />