[FEATURE] VSCode: "Mark all as read" action for the Sessions panel

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

The VSCode extension now shows per-session unread badges and a total unread counter at the bottom of the CHAT / SESSIONS panel (e.g. 12). This is great — but there's no way to clear it in bulk.

When I come back after a few days of activity across many projects, I have 10–20 sessions with unread badges. The only way to get to a clean state today is to click into each session one by one. There is no Claude Code: Mark all sessions as read command in the Command Palette and no header action on the SESSIONS panel for it (the only header icons in v2.1.145 are refresh, search, filter, and layout).

I confirmed this by inspecting the installed extension package (anthropic.claude-code@2.1.145) — no markAsRead, markAllRead, clearUnread, dismissNotification, or resetBadge symbol exists in extension.js or webview/index.js, and package.json declares no related command.

This becomes a real friction point for users who:

• Work across many sessions/projects
• Use background tasks or autonomous loops that finish while away
• Just want a clean inbox without opening every session

Proposed Solution

Add two entry points (either works; both is ideal):

1. Command Palette command: Claude Code: Mark all sessions as read — clears every unread badge and zeros the total counter.
2. Header icon on the SESSIONS panel: an envelope/checkmark icon next to refresh/search/filter/layout, with tooltip "Mark all as read".

Optional polish:

• A right-click context menu item on individual sessions: "Mark as read" / "Mark as unread"
• A scoped variant: "Mark all sessions in this project as read" (since the panel groups by project)

Alternative Solutions

• Today: open each session individually to zero its badge — tedious with 10+ sessions
• Filtering the panel hides old sessions visually but does not clear unread state
• Closing and reopening VSCode does not reset the counter (state is persisted)

Priority

Low — Nice to have

Feature Category

Other (IDE Integration — VSCode extension; the dropdown doesn't have a VSCode category)

Use Case Example

1. I run several long-running tasks across 6 different project folders before lunch
2. I come back to the SESSIONS panel showing 12 unread, distributed across many sessions
3. I've already reviewed the work in another way (PR, terminal output, commit history) and just want to acknowledge the notifications
4. I open the Command Palette → Claude Code: Mark all sessions as read → counter goes to 0
5. Now any new unread badge that appears is a real signal I should act on

Additional Context

• Related (closed/stale, but the feature it requested — unread indicators themselves — appears to have shipped): #34054
• Extension version verified: anthropic.claude-code@2.1.145 on Windows
• Platform: Windows 11, VSCode native extension (not the legacy TUI integration)