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.

backend/app/discover/hero.py

@@ -29,6 +29,10 @@ from app.plex.lookups import by_rating_key
 
 HERO_TIERS = ("resume", "comfort", "surprise")
 
+# How deep the surprise tier draws before giving up. The client's exclusion window is 8 (see
+# `Home.tsx`), so a draw of 12 can always step past a full window of already-shown picks.
+SURPRISE_DRAW = 12
+
 
 def _playable(db: Session, uid: int, card: dict) -> dict | None:
     """A hero has to have a Play button, so a Plex SHOW is resolved to the episode that would start.
@@ -50,22 +54,37 @@ def pick(
     *,
     resume: list[dict] | None = None,
     shelf: list[dict] | None = None,
+    exclude: set[str] | None = None,
 ) -> dict | None:
     """`{"tier": ..., "card": ...}`, or None when nothing at all fits.
 
     `resume` and `shelf` may be passed pre-computed so the consolidated `/api/discover` response does
     not build the same two rails twice; the reroll endpoint passes neither and pays only for what it
-    reaches."""
+    reaches.
+
+    `exclude` is what makes "Mást kérek" mean something. A new seed alone only re-draws the SURPRISE
+    tier: the resume tier deterministically returns the most recently progressed thing that fits, so
+    pressing reroll on a user who has something half-finished handed back the identical card and the
+    button looked dead (measured in the browser, 2026-09-06). Skipping the cards already shown makes
+    every press produce a different answer, at every tier."""
+    skip = exclude or set()
     for card in rails.continue_watching(db, user) if resume is None else resume:
         playable = _playable(db, user.id, card)
+        # Excluded on the card the USER saw (the show), not only on what it resolves to, so a
+        # rerolled-past show does not come straight back as its own next episode.
+        if cards.key(card) in skip or (playable is not None and cards.key(playable) in skip):
+            continue
         if playable is not None and fits(playable["remaining_seconds"], budget):
             return {"tier": "resume", "card": playable}
 
     for card in pins.playables(pins.shelf(db, user) if shelf is None else shelf):
-        if fits(card["remaining_seconds"], budget):
+        if cards.key(card) not in skip and fits(card["remaining_seconds"], budget):
             return {"tier": "comfort", "card": card}
 
-    for card in rails.surprise(db, user, budget, seed, limit=1):
-        return {"tier": "surprise", "card": card}
+    # A wider draw than the one card we need: the shuffle is seeded, so without the headroom an
+    # excluded pick would leave the tier empty rather than move past it.
+    for card in rails.surprise(db, user, budget, seed, limit=SURPRISE_DRAW):
+        if cards.key(card) not in skip:
+            return {"tier": "surprise", "card": card}
 
     return None