Fix final review findings: key leak, model fallback, error resilience, docs

- ApiClient: strip query string from ApiError messages so API keys
  (e.g. TMDb's api_key query param) never leak into 500 response
  bodies or logs.
- LlmTool: accept an optional defaultModel, wired from AppConfig's
  LLM_MODEL, so Langfuse prompts that omit a model config fall back
  to the configured LLM rather than silently requesting gpt-4o-mini.
- RecommendationPipeline: restore the Go original's graceful
  degradation — library/Radarr fetch failures, per-suggestion TMDb
  resolution failures, and per-signal TMDb similarity/recommendation
  failures are now logged and skipped instead of aborting the whole
  run (applies to both runInternal and searchAsync).
- RecommendationsController: validate the ?count= query param
  (must be a positive integer) instead of silently producing NaN.
- Commit the Langfuse prompt definitions (langfuse/*.prompt.json) and
  add a README covering setup, prompt seeding, cache invalidation,
  and the HTTP API surface — the branch was not otherwise runnable by
  anyone but the author.

langfuse/movie-recommender.prompt.json

@@ -0,0 +1,20 @@
+{
+  "name": "movie-recommender",
+  "type": "chat",
+  "prompt": [
+    {
+      "role": "system",
+      "content": "You are a movie recommendation engine. Based on the user's favorite and recently watched movies below, suggest exactly {{count}} movies they would enjoy.\n\nIMPORTANT:\n- Do NOT suggest any movie from the \"Already In Library\" list.\n- Do NOT suggest any movie from the \"Already Suggested\" list.\n- Return ONLY a JSON array, no other text.\n- Each entry: {\"title\": \"Movie Title\", \"year\": 2024, \"reason\": \"brief reason\"}"
+    },
+    {
+      "role": "user",
+      "content": "User's favorite movies:\n{{favorites}}\n\nUser's recently watched movies:\n{{watched}}\n\nAlready in library (DO NOT suggest these):\n{{library}}\n\nAlready suggested (DO NOT repeat these):\n{{previouslySuggested}}"
+    }
+  ],
+  "config": {
+    "model": "llama3",
+    "temperature": 0.7,
+    "maxTokens": 1024
+  },
+  "labels": ["production"]
+}

langfuse/movie-search.prompt.json

@@ -0,0 +1,20 @@
+{
+  "name": "movie-search",
+  "type": "chat",
+  "prompt": [
+    {
+      "role": "system",
+      "content": "You are a movie recommendation engine. Return ONLY a JSON array of {{count}} movies matching the user's request. No other text.\nEach entry: {\"title\": \"Movie Title\", \"year\": 2024, \"reason\": \"brief reason\"}"
+    },
+    {
+      "role": "user",
+      "content": "The user is looking for: {{query}}"
+    }
+  ],
+  "config": {
+    "model": "llama3",
+    "temperature": 0.7,
+    "maxTokens": 1024
+  },
+  "labels": ["production"]
+}