fix: reduce docket redis polling from 250ms to 5s (#559)

the default docket worker polls redis every 250ms (4x/sec), which
caused ~3.4M redis commands in 2 days and $6.73 in upstash costs.

changes:
- add check_interval_seconds and scheduling_resolution_seconds to DocketSettings
- default both to 5 seconds (20x reduction in polling frequency)
- update background.py Worker to use these settings
- update audd costs in export_costs.py ($3.91 -> $9.13 for current period)

expected redis cost reduction: ~95% for idle polling

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-authored-by: Claude <[e-mail]>

backend/src/backend/_internal/background.py

···
 import logging
 from collections.abc import AsyncGenerator
 from contextlib import asynccontextmanager
+from datetime import timedelta
 
 from docket import Docket, Worker
 
···
             async with Worker(
                 docket,
                 concurrency=settings.docket.worker_concurrency,
+                # reduce polling frequency to save Redis costs (default is 250ms)
+                minimum_check_interval=timedelta(
+                    seconds=settings.docket.check_interval_seconds
+                ),
+                scheduling_resolution=timedelta(
+                    seconds=settings.docket.scheduling_resolution_seconds
+                ),
             ) as worker:
                 worker_task = asyncio.create_task(
                     worker.run_forever(),

backend/src/backend/config.py

···
         default=10,
         description="Number of concurrent tasks per worker",
     )
+    check_interval_seconds: float = Field(
+        default=5.0,
+        description="How often to check for new tasks (seconds). Default 5s reduces Redis costs vs docket's 250ms default.",
+    )
+    scheduling_resolution_seconds: float = Field(
+        default=5.0,
+        description="How often to run the scheduler loop (seconds). Default 5s reduces Redis costs vs docket's 250ms default.",
+    )
 
 
 class RateLimitSettings(AppSettingsSection):

scripts/costs/export_costs.py

···
     # the copyright_scans table was created Nov 24 but first scan recorded Nov 30
     # so we hardcode this period from AudD dashboard. DELETE THIS after Dec 24 -
     # future periods will use live database counts.
-    # source: https://dashboard.audd.io - checked 2025-12-09
+    # source: https://dashboard.audd.io - checked 2025-12-10
     "audd": {
-        "total_requests": 6781,
+        "total_requests": 7826,  # 6000 included + 1826 billable
         "included_requests": 6000,  # 1000 + 5000 bonus
-        "billable_requests": 781,
+        "billable_requests": 1826,
         "cost_per_request": 0.005,  # $5 per 1000
-        "cost": 3.91,  # 781 * $0.005
+        "cost": 9.13,  # 1826 * $0.005
         "note": "copyright detection API (indie plan)",
     },
 }