Fix rounds page showing inflated project count

The "537 projects" count was summing projectRoundStates across all
rounds, so a project in 3 rounds was counted 3 times. Now queries
distinct projectIds across all competition rounds to show the actual
unique project count (214).

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

src/app/(admin)/admin/rounds/page.tsx

@@ -283,7 +283,7 @@ export default function RoundsPage() {
   // ─── Main Render ─────────────────────────────────────────────────────────
 
   const activeFilter = filterType !== 'all'
-  const totalProjects = rounds.reduce((s, r) => s + r._count.projectRoundStates, 0)
+  const totalProjects = (compDetail as any)?.distinctProjectCount ?? 0
   const totalAssignments = rounds.reduce((s, r) => s + r._count.assignments, 0)
   const activeRound = rounds.find((r) => r.status === 'ROUND_ACTIVE')
 

src/server/routers/competition.ts

@@ -122,7 +122,17 @@ export const competitionRouter = router({
         throw new TRPCError({ code: 'NOT_FOUND', message: 'Competition not found' })
       }
 
-      return competition
+      // Count distinct projects across all rounds (not sum of per-round states)
+      const roundIds = competition.rounds.map((r) => r.id)
+      const distinctProjectCount = roundIds.length > 0
+        ? await ctx.prisma.projectRoundState.findMany({
+            where: { roundId: { in: roundIds } },
+            select: { projectId: true },
+            distinct: ['projectId'],
+          }).then((rows) => rows.length)
+        : 0
+
+      return { ...competition, distinctProjectCount }
     }),
 
   /**