feat(planning): hidden-tab title badge on the interview page

[kyle-sexton]

Problem

The interview page sets a static title (plugins/planning/surface/index.html:737), so a hidden tab gives no signal that a reply or update is waiting. This is the stale-tab report in handoff item 20260926-100300.

Evidence

index.html:737 sets the title once; nothing changes it when the tab is hidden.

Proposed approach

While the document is hidden and something new needs the user (for example a reply or an updated notice), prefix the title with a badge; clear it when the tab becomes visible. Use the Page Visibility API.

Acceptance criteria

• A hidden tab shows a badge in document.title when new activity arrives.
• The badge clears when the tab is shown.
• The static title is unchanged otherwise.

Context

Refs #4653 (owner decision 2026-09-29, Option B).