[FEATURE] Always show session identifier in status line, even before /rename

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

After /rename, the session name appears in the bottom-right status line with a distinct color, which is very helpful for identifying which session I'm in. However, before manually running /rename, the status line shows no session identifier at all.

When working with multiple sessions (e.g. via /resume), there is no visual cue to distinguish sessions until you manually name each one. This creates friction — you have to remember to /rename every session, or lose track of which session you're in.

Proposed Solution

Always display a session identifier in the status line, even before the user runs /rename. This could be:

1. An auto-generated summary name (similar to what /rename without arguments produces) created at session start
2. A short session ID or hash as a fallback when no name is set
3. A truncated first-message summary

The key behavior: the status line slot for session name should never be empty when a session is active.

Alternative Solutions

• A setting like statusLine.alwaysShowSessionName: true that users can opt into
• Auto-run the equivalent of /rename (no args) after the first user message, so every session gets a name without manual intervention

Additional Context

Related closed issue: #15267 (exposing session name to statusLine JSON input)