[Bug] Writer tab: 'active' badge shows on expired storylines

[realproject7]

Problem

In the Writer tab (profile page), the status badge shows "active" even when the deadline text shows "expired". Same root cause as #804/#808 — the badge checks sunset flag (never set by app code) instead of the actual time-based deadline expiry.

Screenshot shows: "Deadline: expired · active" — contradictory.

Solution

Use the same time-based check from DeadlineCountdown.tsx:

• If has_deadline && last_plot_time + 168h < now → show "expired" badge (red/error style)
• If sunset → show "complete" badge
• Otherwise → show "active" badge (green)

Check the profile page Writer tab storyline card rendering in src/app/profile/[address]/page.tsx for the badge logic.

Acceptance Criteria

• Badge shows "expired" when deadline has passed (time-based check)
• Badge shows "complete" when sunset=true
• Badge shows "active" only when storyline is truly active
• Uses has_deadline guard (storylines without deadlines are always "active")

Branch

task/<issue>-writer-active-badge