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/api/endpoints/timeline.py

@@ -106,6 +106,13 @@ Return ONLY a valid JSON object with "decades" and "insight" keys. No other text
             messages=[{"role": "user", "content": prompt}],
         )
 
+        # Track API cost (Haiku: $0.80/M input, $4/M output)
+        api_logger = logging.getLogger("app")
+        input_tokens = message.usage.input_tokens
+        output_tokens = message.usage.output_tokens
+        cost = (input_tokens * 0.80 / 1_000_000) + (output_tokens * 4 / 1_000_000)
+        api_logger.info(f"API_COST|model=claude-haiku|input={input_tokens}|output={output_tokens}|cost=${cost:.4f}|user={user.id}|endpoint=timeline")
+
         response_text = message.content[0].text.strip()
 
         # Try to extract JSON if wrapped in markdown code blocks