perf(realtime+data): implement perf-data-optimization and perf-realtime-scale

## perf-data-optimization
- Add @@index([name]) on User model (migration)
- Add WEATHER_HISTORY_LIMIT=90 constant, apply take/orderBy on weather history queries
- Replace deep includes with explicit select on all 6 list service queries
- Add unstable_cache layer with revalidateTag on all list service functions
- Add cache-tags.ts helpers (sessionTag, sessionsListTag, userStatsTag)
- Invalidate sessionsListTag in all create/delete Server Actions

## perf-realtime-scale
- Create src/lib/broadcast.ts: generic createBroadcaster factory with shared polling
  (one interval per active session, starts on first subscriber, stops on last)
- Migrate all 6 SSE routes to use createBroadcaster — removes per-connection setInterval
- Add broadcastToXxx() calls in all Server Actions after mutations for immediate push
- Add SESSIONS_PAGE_SIZE=20, pagination on sessions page with loadMoreSessions action
- Add "Charger plus" button with loading state and "X sur Y" counter in WorkshopTabs

## Tests
- Add 19 unit tests for broadcast.ts (polling lifecycle, userId filtering,
  formatEvent, error resilience, session isolation)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/app/sessions/page.tsx

@@ -26,6 +26,7 @@ import {
 } from '@/services/gif-mood';
 import { Card, PageHeader } from '@/components/ui';
 import { withWorkshopType } from '@/lib/workshops';
+import { SESSIONS_PAGE_SIZE } from '@/lib/types';
 import { WorkshopTabs } from './WorkshopTabs';
 import { NewWorkshopDropdown } from './NewWorkshopDropdown';
 
@@ -84,13 +85,23 @@ export default async function SessionsPage() {
     getTeamGifMoodSessions(session.user.id),
   ]);
 
-  // Add workshopType to each session for unified display
-  const allSwotSessions = withWorkshopType(swotSessions, 'swot');
-  const allMotivatorSessions = withWorkshopType(motivatorSessions, 'motivators');
-  const allYearReviewSessions = withWorkshopType(yearReviewSessions, 'year-review');
-  const allWeeklyCheckInSessions = withWorkshopType(weeklyCheckInSessions, 'weekly-checkin');
-  const allWeatherSessions = withWorkshopType(weatherSessions, 'weather');
-  const allGifMoodSessions = withWorkshopType(gifMoodSessions, 'gif-mood');
+  // Track totals before slicing for pagination UI
+  const totals = {
+    swot: swotSessions.length,
+    motivators: motivatorSessions.length,
+    'year-review': yearReviewSessions.length,
+    'weekly-checkin': weeklyCheckInSessions.length,
+    weather: weatherSessions.length,
+    'gif-mood': gifMoodSessions.length,
+  };
+
+  // Add workshopType and slice first page
+  const allSwotSessions = withWorkshopType(swotSessions.slice(0, SESSIONS_PAGE_SIZE), 'swot');
+  const allMotivatorSessions = withWorkshopType(motivatorSessions.slice(0, SESSIONS_PAGE_SIZE), 'motivators');
+  const allYearReviewSessions = withWorkshopType(yearReviewSessions.slice(0, SESSIONS_PAGE_SIZE), 'year-review');
+  const allWeeklyCheckInSessions = withWorkshopType(weeklyCheckInSessions.slice(0, SESSIONS_PAGE_SIZE), 'weekly-checkin');
+  const allWeatherSessions = withWorkshopType(weatherSessions.slice(0, SESSIONS_PAGE_SIZE), 'weather');
+  const allGifMoodSessions = withWorkshopType(gifMoodSessions.slice(0, SESSIONS_PAGE_SIZE), 'gif-mood');
 
   const teamSwotWithType = withWorkshopType(teamSwotSessions, 'swot');
   const teamMotivatorWithType = withWorkshopType(teamMotivatorSessions, 'motivators');
@@ -150,6 +161,7 @@ export default async function SessionsPage() {
             weeklyCheckInSessions={allWeeklyCheckInSessions}
             weatherSessions={allWeatherSessions}
             gifMoodSessions={allGifMoodSessions}
+            totals={totals}
             teamCollabSessions={[
               ...teamSwotWithType,
               ...teamMotivatorWithType,