feat(e24): the Home surface — one question, one answer, both sources

E24 S2. A new `home` module in layout C+ (the mockup the owner picked): the
time-budget chips on top, one large hero that answers them, then the comfort
shelf and a cross-source resume rail. Home is the landing — deliberately OVER
the remembered last module, since landing on whatever you happened to close the
app on is the habit this epic exists to replace; `LS.startOnHome = "0"` opts an
account back out (Settings toggle lands in S4).

No third card component: each unified card carries the native feed / Plex
payload, so the rails render through the existing VideoCard (`cardsSmall`) and
PlexPosterCard, and `aspect` decides the tile shape without branching on source.
Plex playback hands off to the Plex module via a new `jumpTo` type — the player
lives there with its lazy hls.js and its provider tree, and mounting a second one
on the landing page to save one hand-off would be the expensive way round.

Four defects found by driving it in a real browser against the live account, each
now pinned by a mutation-checked test:

- **The reroll gave the same card back.** A new seed only re-draws the SURPRISE
  tier; the resume tier deterministically returns the most recently progressed
  thing that fits, so anyone with something half-finished pressed a dead button.
  `/pick` now takes an `exclude` list of `<source>:<id>` keys and the client keeps
  a rolling window of 8. Excluding a SHOW also excludes the episode it resolves
  to — otherwise the same suggestion comes back wearing a hat.
- **"Nothing to suggest yet" flashed over a full library** whenever a reroll was
  in flight: the new query key has no data for a beat. An empty state standing in
  for a loading one is the dishonesty the house rules name outright. The hero now
  falls back to the loaded payload while a pick is pending, and only trusts a null
  once the pick has RESOLVED.
- **A budget change replaced the page — chips included — with a spinner**, so the
  control you just clicked vanished under your cursor. `keepPreviousData`, the
  same reason the feed uses it.
- **The hero printed twice**, once as itself and once as the first resume tile.

Two smaller UI calls made from the same session: the budget caption sits NEXT to
its chips rather than in SegmentedToggle's justify-between mode, which on an 80rem
page throws the answers to the far edge; and the feed takes the YouTube mark its
own toolbar already uses, since Home now owns the house icon.

Gate green: ruff, ruff format, 3x tsc, eslint, prettier, knip, vitest 780,
pytest 989. Verified end to end on localdev against the real account: budget
chips re-answer (matched on REMAINING time — a 51-minute video with 2:46 left is
a ten-minute answer), the reroll walks three distinct heroes, and a Plex show
tile opens its drill-down in the Plex module.

frontend/src/lib/api.ts

@@ -32,6 +32,9 @@ import { setupApi } from "./api/setup";
 export type * from "./api/setup";
 import { feedApi } from "./api/feed";
 export type * from "./api/feed";
+import { discoverApi } from "./api/discover";
+export type * from "./api/discover";
+export { DISCOVER_BUDGETS, PIN_KINDS, discoverCardKey } from "./api/discover";
 export type * from "./api/tagModes";
 export {
   DEFAULT_TAG_MODES,
@@ -77,6 +80,7 @@ export const api = {
   ...authApi,
   ...setupApi,
   ...feedApi,
+  ...discoverApi,
   ...channelsApi,
   ...syncApi,
   ...playlistsApi,