[FEATURE] Desktop: open a session from its notification in split view or a new window

### Preflight Checklist

- [x] I have searched [existing requests](https://github.com/anthropics/claude-code/issues?q=is%3Aissue%20label%3Aenhancement) and this feature hasn't been requested yet
- [x] This is a single feature request (not multiple features)

### Problem Statement

I run several Code sessions side by side in split view. When a session I'm not looking at needs me (a permission prompt or a question), the desktop app shows a notification. Clicking it opens that session in the pane I'm working in, replacing it. I lose my place, deal with the other session, then have to find my way back to what I was doing.

Split view already handles this well from the sidebar: Option+click, ⋮ → Open in → Split view, or dragging a session opens it as a tile beside the current one, and closing that tile lets the other tiles reflow. None of that is reachable from the notification, though, and the notification is what's in front of me at the moment I need to act.

### Proposed Solution

Let the notification open the session beside the current one, using the actions the sidebar already has:

1. **Same modifiers as the sidebar.** Option+click on the notification opens the session in a split pane, and Cmd+click opens it in its own window. A plain click keeps today's behaviour.
2. **A setting** under Settings → Claude Code: *Open sessions from notifications in*: `Current pane` (today's behaviour) / `Split view` / `New window`.
3. **Reuse an open tile.** If the session is already showing in a split pane, focus that pane instead of replacing the one I'm in.

The flow then becomes: notification arrives, click it, the session opens beside mine, I approve or answer, Close Split View (Ctrl+Cmd+W), and the layout is back to how it was.

### Alternative Solutions

Ignore the notification, find the session in the sidebar by its attention marker, and Option+click it (or use ⋮ → Open in → Split view). It works, but it's slower, and the natural thing to do, clicking the notification, throws away the current layout.

### Priority

Medium - Would be very helpful

### Feature Category

Configuration and settings

### Use Case Example

1. Three sessions are tiled in split view and I'm working in one of them.
2. A notification says another session needs approval to run a command.
3. I click it and that session opens as a new tile beside mine.
4. I approve, close the tile with Ctrl+Cmd+W, and the other tiles reflow. I never left the session I was working in.

### Additional Context

- Related: #86925 asks for a setting to make split view the default for sidebar clicks. This request covers the notification entry point, and the two settings could sit together.
- Claude desktop 1.46388.4 on macOS 26.5.1.
- Small docs mismatch while you're in this area: https://code.claude.com/docs/en/desktop says Cmd+click on a sidebar session opens a split pane. In the current build Cmd+click opens the session in its own window and Option+click opens the split.

Start by reading the desktop notification behavior and existing sidebar Open in actions described in the issue, then review related issue #86925 and the linked desktop documentation for current modifier mappings. Trace the Settings → Claude Code entry point and notification click path. Done means notification clicks support the requested plain-click, modifier, setting, and reuse behavior without losing the current split layout.

Written by the indexing model from the issue text.