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/tests/test_discover.py

@@ -356,6 +356,62 @@ def test_the_seed_decides_which_source_leads(db):
     assert leaders == {"youtube", "plex"}
 
 
+def test_the_reroll_must_be_able_to_move_past_the_resume_tier(db):
+    """A new seed alone only re-draws the SURPRISE tier — the resume tier deterministically returns
+    the most recently progressed thing that fits, so without an exclusion the reroll handed the same
+    card straight back and the button looked dead (found in the browser, 2026-09-06)."""
+    user, _ = _seed_yt(db)
+    db.add_all(
+        [
+            VideoState(
+                user_id=user.id,
+                video_id="vmed",
+                status="new",
+                position_seconds=300,
+                progress_updated_at=NOW,
+            ),
+            VideoState(
+                user_id=user.id,
+                video_id="vshort",
+                status="new",
+                position_seconds=60,
+                progress_updated_at=NOW - timedelta(hours=1),
+            ),
+        ]
+    )
+    db.commit()
+
+    first = hero.pick(db, user, "any", seed=1)
+    assert first["card"]["id"] == "vmed"
+    # Same seed, same everything — only the exclusion differs.
+    second = hero.pick(db, user, "any", seed=1, exclude={"youtube:vmed"})
+    assert second["card"]["id"] == "vshort"
+
+
+def test_excluding_a_show_also_excludes_the_episode_it_resolves_to(db):
+    """The user rerolled past the SHOW they were shown; handing back its next episode under a
+    different title would be the same suggestion wearing a hat."""
+    user, _ = _seed_yt(db)
+    _, show, ep1 = _seed_plex(db, user)
+    _enable_plex(db)
+    db.add(
+        PlexState(
+            user_id=user.id,
+            item_id=ep1.id,
+            status="new",
+            position_seconds=120,
+            progress_updated_at=NOW,
+        )
+    )
+    db.commit()
+
+    shown = hero.pick(db, user, "any", seed=1)
+    assert shown["card"]["id"] == "ps1e1"  # the show resolved to its in-progress episode
+    # Excluding what the USER saw — the show — must move the tier on, not return the episode again.
+    after = hero.pick(db, user, "any", seed=1, exclude={"plex:ps1"})
+    assert after is None or after["card"]["id"] != "ps1e1"
+
+
 # ── comfort shelf ─────────────────────────────────────────────────────────────────────────────────