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/app/tournament/[code]/page.tsx

@@ -1,5 +1,6 @@
 "use client";
 
+import InviteFriendsModal from "@/components/InviteFriendsModal";
 import { useSession } from "@/context/session";
 import { fetchTournament, joinTournament, startTournament } from "@/lib/tournament";
 import type { Tournament, TournamentRound } from "@michess/types";
@@ -109,7 +110,7 @@ export default function TournamentDetailPage() {
             )}
           </div>
         </div>
-        <div className="flex gap-2">
+        <div className="flex gap-2 flex-wrap">
           {tournament.status === "waiting" && user?.id && !isJoined && (
             <button
               className={"btn btn-secondary btn-sm" + (actionLoading ? " loading" : "")}
@@ -119,6 +120,9 @@ export default function TournamentDetailPage() {
               Beitreten
             </button>
           )}
+          {tournament.status === "waiting" && isJoined && (
+            <InviteFriendsModal gameCode={`tournament/${code}`} label="Freunde einladen" />
+          )}
           {canStart && (
             <button
               className={"btn btn-primary btn-sm" + (actionLoading ? " loading" : "")}