Add game end status with an end_game DM tool and automatic 0-HP detection

Games now have a status/ended_reason pair. The DM can call the new
end_game tool when the story reaches a real conclusion (victory,
defeat, or a resolved one-shot), and the backend independently ends
the game whenever a character's HP drops to 0 or below, regardless of
whether the DM narrates it. The frontend shows a banner and a
"Beendet" badge once a game ends.

HP moves from the freeform combat_stats bag into dedicated
current_hp/max_hp columns on Character, since reliably detecting 0 HP
requires a real integer rather than parsing strings like "3/10" out of
an LLM-authored key/value dict. Also fixed combat_stats to fully
replace on each upsert instead of merging, matching its documented
contract — the merge was leaving stale keys (old HP/TP text) behind
after the model stopped sending them.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

backend/app/llm/tools/end_game.py

@@ -0,0 +1,40 @@
+import uuid
+
+from sqlalchemy.ext.asyncio import AsyncSession
+
+from app.models.game import Game
+
+TOOL_SCHEMA = {
+    "name": "end_game",
+    "description": (
+        "Call when the story reaches a real conclusion — the party wins, loses, or a one-shot's "
+        "plot is resolved. Marks the game as ended so players see a clear ending. Do not call this "
+        "just because a scene ends; only for a genuine story conclusion."
+    ),
+    "parameters": {
+        "type": "object",
+        "properties": {
+            "reason": {
+                "type": "string",
+                "description": (
+                    "A short narrative summary of how/why the story ended (victory, defeat, or "
+                    "resolution), shown to the players, e.g. 'Das Dorf ist gerettet, die Kerze brennt wieder.'"
+                ),
+            },
+        },
+        "required": ["reason"],
+    },
+}
+
+
+async def end(session: AsyncSession, game_id: uuid.UUID, tool_input: dict) -> dict:
+    game = await session.get(Game, game_id)
+    if game is None:
+        raise ValueError(f"Game {game_id} not found")
+
+    if game.status != "ended":
+        game.status = "ended"
+        game.ended_reason = tool_input["reason"]
+        await session.commit()
+
+    return {"status": "ended", "reason": game.ended_reason}