Freegle / Iznik / 23907

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fix(site,modtools): keep the browser-tab unread badge live (9806/9)

The unread-count tab badge stopped updating between page loads. useHead's
titleTemplate is a plain function, so Nuxt does NOT re-run it when the count refs
read inside it change — the badge only refreshed on navigation. ModTools fared a
bit better but only because its work poll rewrote document.title every 30s, so it
still lagged behind incoming chats. Reporter (Neville, 9806/9): a chat reply
arrived and showed a red chat badge, but the tab count stayed empty until he
clicked the chat (a navigation, which re-ran titleTemplate).

Add useReactiveTabBadge(getter): a client-side watcher that re-applies the
"(N) " prefix to document.title the moment the count changes, alongside the
existing useHead (which still sets the per-page base title). Wired into both the
Freegle site (app.vue) and ModTools (modtools/app.vue). The prefix logic is a
pure, tested applyBadgeToTitle(currentTitle, total) helper.

Vitest green (13545).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013zGET5BRtdWbRc2nsf1Lss

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