feat: implement variable team matchups with partner rotation

- Add manual team entry for permanent teams in Matchups tab
- Rename 'Teams' tab to 'Matchups' for clarity
- Implement partner rotation strategies (minimize_repeat, maximize_even, elo_based)
- Track partnerships across rounds to minimize repeat pairings
- Fix unit tests for team configuration and ELO calculations
- Add E2E test for 9+ participant tournaments with variable matchups

Key changes:
- TeamsSection.tsx: Added router.refresh(), manual team entry, and matchup display
- schedule-generator.ts: Enhanced generateVariableRoundRobin to track partnerships
- team-generator.ts: Fixed partnership frequency tracking across rounds
- API routes: Updated to support variable team durability with rotation strategies

src/app/api/players/route.ts

@@ -30,3 +30,64 @@ export async function GET() {
     );
   }
 }
+
+/**
+ * POST /api/players
+ * 
+ * Create a new player
+ * This is a public endpoint (no authentication required)
+ * Returns 409 if player with same name already exists
+ */
+export async function POST(request: Request) {
+  try {
+    const body = await request.json();
+    const { name } = body;
+
+    // Validate name
+    if (!name || typeof name !== 'string' || name.trim().length === 0) {
+      return NextResponse.json(
+        { error: "Player name is required" },
+        { status: 400 }
+      );
+    }
+
+    const trimmedName = name.trim();
+    const normalizedName = trimmedName.toLowerCase();
+
+    // Check if player with same name already exists
+    const existingPlayer = await prisma.player.findUnique({
+      where: { normalizedName },
+    });
+
+    if (existingPlayer) {
+      return NextResponse.json(
+        { error: `Player "${trimmedName}" already exists` },
+        { status: 409 }
+      );
+    }
+
+    // Create new player
+    const newPlayer = await prisma.player.create({
+      data: {
+        name: trimmedName,
+        normalizedName,
+        currentElo: 1000,
+        gamesPlayed: 0,
+        wins: 0,
+        losses: 0,
+      },
+    });
+
+    return NextResponse.json(
+      { success: true, player: newPlayer },
+      { status: 201 }
+    );
+  } catch (error: unknown) {
+    console.error("Error creating player:", error);
+    const message = error instanceof Error ? error.message : "Failed to create player";
+    return NextResponse.json(
+      { error: message },
+      { status: 500 }
+    );
+  }
+}