feat(picker): wire shuffle action to /api/shuffle

[sudoesnothing]

What

Replaces the picker's local shuffle stub with a real POST /api/shuffle
round-trip (backend shipped across #47, #54, #56, #58).

• handleShuffle now POSTs {playlistId}, validates the response shape,
  and maps 8 error codes to ErrorKind via mapShuffleError.
• A 1000ms phase-flip (cancel-on-settle) prevents "Saving new playlist…"
  from flashing on fast round-trips before "Done." lands.
• Error view gains a four-way CTA: session expiry goes to login; unshuffleable
  playlists get "Pick another" (restores picker, no refetch); shuffle failures
  with a source set get "Try again" (re-POSTs the same playlist id); load-path
  errors keep the existing reloadKey bump.
• LoadState's error variant now carries optional source / playlists to
  support the above without a refetch on either recovery path.

Why

The backend has been live against real Spotify for a week; wiring the picker
now is the natural close of the round-trip.

The source-aware retry is the meaningful design call here. The existing
reload-picker behavior makes a user re-find their playlist in a long list
after every rate-limit or transient error. Carrying source through the
error round-trip lets "Try again" re-POST the same playlist directly.
playlists travels with the error for the same reason: "Pick another" can
restore the picker without paying a refetch.

Test plan

• Real Spotify auth: click Shuffle on Liked Songs and confirm a new
  shuffled playlist with the expected name suffix appears in the library.
• Click Shuffle on a normal playlist and confirm the resulting playlist
  carries the correct Shuffled YYYY-MM-DD suffix in the Spotify app.
• Trigger a non-trivial error path against a live network (kill network
  mid-shuffle for an upstream error, or expire the session cookie) and
  confirm the correct CTA renders.