perf(feed): a shuffle walks a stored random key instead of sorting the whole scope

Every video carries a random number drawn once (videos.shuffle_key, migration 0118, indexed with
id). A seed picks a point on that ring: the feed's Shuffle sort pages along it and wraps, and the
Home surprise reads a 500-video window of it and shuffles that window by the seed, so no video is
favoured for sitting after a wide gap. The md5(id || seed) order read and sorted the whole feed
scope on every call: ~350 ms on prod per surprise, 381-767 ms per Shuffle page on localdev, now
14 ms and 4 ms.

backend/app/catalog/models.py

@@ -10,6 +10,7 @@ from sqlalchemy import (
     Boolean,
     Computed,
     DateTime,
+    Float,
     ForeignKey,
     Integer,
     JSON,
@@ -217,6 +218,9 @@ class Video(Base, TimestampMixin):
     last_checked_at: Mapped[datetime | None] = mapped_column(DateTime(timezone=True))
     unavailable_since: Mapped[datetime | None] = mapped_column(DateTime(timezone=True))
     unavailable_reason: Mapped[str | None] = mapped_column(String(24))
+    # A random number in [0, 1), drawn once when the row is written: the ring a seeded shuffle walks
+    # (`feedquery.shuffle_walk`, index ix_videos_shuffle_key on (shuffle_key, id), migration 0118).
+    shuffle_key: Mapped[float] = mapped_column(Float, nullable=False, server_default=func.random())
 
     @hybrid_property
     def length_seconds(self) -> int | None: