feat: add friend invite modal to all game modes

- New InviteFriendsModal component: fetches friends list, sends game
  invite via notification socket with per-friend sent confirmation
- Multiplayer (GamePage): invite button below copy link, hidden after game ends
- Correspondence: invite button in waiting-for-opponent card
- Tournament: invite button for joined players while status is waiting
- Invite links use mode-prefixed codes (correspondence/XYZ, tournament/XYZ)
  so notification "Beitreten" button navigates to the correct page

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

client/src/components/InviteFriendsModal.tsx

@@ -0,0 +1,90 @@
+"use client";
+
+import { API_URL } from "@/config";
+import { useNotifications } from "@/context/NotificationContext";
+import { useSession } from "@/context/session";
+import { useState } from "react";
+
+interface Friend {
+  id: number;
+  friend_id: number;
+  friend_name: string;
+}
+
+export default function InviteFriendsModal({
+  gameCode,
+  label = "Freunde einladen"
+}: {
+  gameCode: string;
+  label?: string;
+}) {
+  const { user } = useSession();
+  const { sendGameInvite } = useNotifications();
+  const [open, setOpen] = useState(false);
+  const [friends, setFriends] = useState<Friend[]>([]);
+  const [loading, setLoading] = useState(false);
+  const [sent, setSent] = useState<Record<number, boolean>>({});
+
+  async function openModal() {
+    if (!user?.id || typeof user.id === "string") return;
+    setOpen(true);
+    setLoading(true);
+    const res = await fetch(`${API_URL}/v1/friends`, { credentials: "include" });
+    if (res.ok) setFriends(await res.json());
+    setLoading(false);
+  }
+
+  function invite(friendId: number) {
+    sendGameInvite(friendId, gameCode);
+    setSent((prev) => ({ ...prev, [friendId]: true }));
+    setTimeout(() => setSent((prev) => ({ ...prev, [friendId]: false })), 3000);
+  }
+
+  if (!user?.id || typeof user.id === "string") return null;
+
+  return (
+    <>
+      <button className="btn btn-sm btn-outline" onClick={openModal}>
+        {label}
+      </button>
+
+      {open && (
+        <dialog className="modal modal-open">
+          <div className="modal-box max-w-sm">
+            <button
+              className="btn btn-sm btn-circle btn-ghost absolute right-2 top-2"
+              onClick={() => setOpen(false)}
+            >
+              ✕
+            </button>
+            <h3 className="font-bold text-lg mb-4">{label}</h3>
+            {loading ? (
+              <div className="flex justify-center py-4">
+                <span className="loading loading-spinner" />
+              </div>
+            ) : friends.length === 0 ? (
+              <p className="text-sm opacity-60">
+                Keine Freunde gefunden. Füge zuerst Freunde hinzu.
+              </p>
+            ) : (
+              <div className="flex flex-col gap-3">
+                {friends.map((f) => (
+                  <div key={f.id} className="flex items-center justify-between gap-2">
+                    <span className="font-medium">{f.friend_name}</span>
+                    <button
+                      className={"btn btn-sm btn-secondary" + (sent[f.friend_id] ? " btn-success" : "")}
+                      onClick={() => invite(f.friend_id)}
+                    >
+                      {sent[f.friend_id] ? "✓ Gesendet" : "Einladen"}
+                    </button>
+                  </div>
+                ))}
+              </div>
+            )}
+          </div>
+          <div className="modal-backdrop bg-black/40" onClick={() => setOpen(false)} />
+        </dialog>
+      )}
+    </>
+  );
+}