Add API cost tracking to admin dashboard

Track estimated Anthropic API costs per request across all Claude API
call sites (recommender, analyze, artist-dive, generate-playlist, crate,
rabbit-hole, playlist-fix, timeline, compatibility). Log token usage and
estimated cost to the app logger. Aggregate costs in admin stats endpoint
and display total/today costs and token usage in the admin dashboard.

backend/app/services/recommender.py

@@ -238,6 +238,15 @@ Return ONLY the JSON array, no other text."""
         messages=[{"role": "user", "content": prompt}],
     )
 
+    # Track API cost
+    import logging
+    api_logger = logging.getLogger("app")
+    input_tokens = message.usage.input_tokens
+    output_tokens = message.usage.output_tokens
+    # Sonnet pricing: $3/M input, $15/M output
+    cost = (input_tokens * 3 / 1_000_000) + (output_tokens * 15 / 1_000_000)
+    api_logger.info(f"API_COST|model=claude-sonnet|input={input_tokens}|output={output_tokens}|cost=${cost:.4f}|user={user.id}|endpoint=generate_recommendations")
+
     # Parse response
     response_text = message.content[0].text.strip()
     # Handle potential markdown code blocks