fix(e24): the Home surface's three UAT findings — Back, the reroll, and a show card

All three were measured before they were touched, and the diagnosis moved twice.

**Back from a Plex title played off Home landed on the Plex module's root.** One
click pushed three history entries: the page navigation, the sub-view opened by
the `jumpTo` hand-off, and — under StrictMode, whose effect body runs twice
before `setJumpTo(null)` re-renders — that same sub-view a second time. So the
first Back visibly did nothing and the second stranded the user on a Discover
page they had never visited.

A cross-module hand-off is the CONTINUATION of the navigation that brought you
there, not a second navigation, so it now REPLACES the page entry instead of
stacking on it (`useHistorySubview.open(view, {replace})`, asked for by the jump
target). Replacing is also idempotent, which is what disarms the StrictMode
double-run. The intent rides on `PlexJumpTarget` rather than being inferred,
because the header typeahead jumps from INSIDE the module, where the entry being
replaced would be a sub-view the user really was looking at.

**"Mást kérek" cycled nine cards and never left the resume tier.** Measured:
twelve presses, nine distinct titles, period nine, every one `tier: "resume"` —
the shelf and the surprise tier were unreachable by pressing the button. Two
causes multiplied: the tiers were tried in a fixed priority order over a 20-row
resume rail, so the button just walked down it; and the client's rolling
exclusion window of 8 guaranteed the wrap.

The press count now rotates which tier answers first (`start`), so each press
offers a different KIND of answer — the user's call, given the choice between
that, a wider window, and a surprise-only reroll. The fallthrough is kept, so a
press does not come back empty because the tier it led with had nothing. The
window is matched to the server's own cap rather than a smaller number of ours.

**A half-watched series on Home opened the show page.** A movie already went
straight to the player; only shows did not — and the comfort shelf and the hero
both resolved a show to its next episode while this rail alone did not, handing
back six seasons to choose between. The rail row now carries `next`, and the
client already played `next ?? card`, so this is a backend fix.

Affording it needed `queries.next_episode` to stop loading every episode of the
show into Python to pick one of them (236 rows for Friends, 227 for JAG) — three
ordered LIMIT 1 probes instead. The show→episode rule now lives in ONE function
(`rails.playable`), which is what the shelf, the hero and the rail all call; two
implementations are how they came to disagree.

Ten mutations run, all ten red for the right test — including a first pass where
the press count reached `api.discoverPick` and stopped there, invisible because
every Home test mocks that module. The slice now has its own URL test.

Verified in a clean browser tab against the live account: one Back returns to
Home, the rotation gives resume/comfort/surprise across nine presses with no
repeat, and Westworld opens at S1E1 rather than at its show page.

backend/app/discover/rails.py

@@ -13,7 +13,8 @@ from sqlalchemy.orm import Session
 from app import sysconfig
 from app.discover import cards, queries
 from app.discover.queries import RAIL_LIMIT
-from app.models import User
+from app.models import PlexShow, User
+from app.plex.lookups import by_rating_key
 
 # Sort sentinel for a row whose timestamp is missing. A plain `(ts is not None, ts)` key looks like it
 # handles NULLs and does not: two NULL rows compare equal on the flag and then compare `None < None`,
@@ -27,18 +28,49 @@ def plex_available(db: Session) -> bool:
     return sysconfig.get_bool(db, "plex_enabled")
 
 
+def playable(db: Session, uid: int, card: dict) -> dict | None:
+    """The thing that would actually START from this card — itself for anything with a runtime, and
+    for a Plex SHOW the episode that is next (in progress, else the first unwatched, else the first).
+
+    ONE function, because three surfaces need the same answer and a second implementation is how the
+    shelf and the rail came to disagree in the first place: the hero calls it to decide what it is
+    offering, `continue_watching` calls it to fill each show tile's `next`, and the comfort shelf
+    resolves the same way in `pins`. None when the show has no episodes mirrored yet.
+
+    A card that already carries a resolved `next` (a rail row) is taken at its word rather than
+    re-queried — the hero reads the rail it was handed."""
+    if not (card.get("source") == "plex" and card.get("kind") == "show"):
+        return card
+    if "next" in card:
+        return card["next"]
+    sh = by_rating_key(db, PlexShow, card["id"])
+    if sh is None:
+        return None
+    ep = queries.next_episode(db, uid, sh.id)
+    return cards.from_plex(ep) if ep else None
+
+
 def continue_watching(db: Session, user: User, limit: int = RAIL_LIMIT) -> list[dict]:
     """One resume rail across both sources, most recently progressed first.
 
-    A Plex SHOW enters as a show card (that is what the Plex rail shows too, and it is what the user
-    recognises); resolving it to an episode is the hero's job, where something actually has to play."""
+    A Plex SHOW enters as a show CARD — that is what the Plex rail shows, and it is the artwork the
+    user recognises — but it carries `next`: the episode that would actually start. Without it a
+    click on a half-watched series landed on the show page with six seasons to choose between, which
+    is the decision this whole surface exists to remove (the comfort shelf and the hero already
+    resolved; only this rail did not). The client plays `next ?? card`, so the tile stays a poster and
+    the click stays one click."""
     rows: list[tuple[object, dict]] = [
         (ts, cards.from_video(r)) for ts, r in queries.yt_in_progress(db, user, limit)
     ]
     if plex_available(db):
         rows += [(ts, cards.from_plex(c)) for ts, c in queries.plex_in_progress(db, user.id, limit)]
     rows.sort(key=lambda r: r[0] or _NO_TS, reverse=True)
-    return [card for _, card in rows[:limit]]
+    out = [card for _, card in rows[:limit]]
+    # Resolve AFTER the slice: only the rows that survive it are worth a query.
+    for card in out:
+        if card["kind"] == "show":
+            card["next"] = playable(db, user.id, card)
+    return out
 
 
 def surprise(db: Session, user: User, budget: str, seed: int, limit: int = 3) -> list[dict]: