refactor(ui): reuse the store, media-query and deleted-tag rules the review found rebuilt, and name a loading pick

E32 review round 1 (F3–F6).

- Channels' open-row store and the chat dock use lib/store's createStore instead of a hand-rolled
  listener set (the chat dock gets a test of its own).
- The Plex backdrop reads prefers-reduced-motion through useMediaQuery; the query string is one
  constant (REDUCED_MOTION) for the hook and the carousel's one-off read.
- A link-restored collection filter showed its raw rating_key in the picker while the titles
  loaded: usePlexCollectionTitles now says it is pending, the picker draws a placeholder
  (labelsPending, as the channel picker does) and so does the chip row.
- The "deleted tag" rule was written twice with two i18n keys and had drifted: the channel manager
  showed NO chip for a pick while the tag list loaded, or ever after a failed load, while the pick
  still narrowed the table. One rule now (lib/tagPicks), one key (common.deletedTag); the manager's
  row shows every pick, as a placeholder while loading and as its id after a failure.

frontend/src/components/ui/Carousel.tsx

@@ -6,6 +6,7 @@ import { useScrollEdges } from "../../lib/useScrollEdges";
 import { useListNav } from "../../lib/listNav";
 import { Button } from "./Button";
 import { IconButton } from "./IconButton";
+import { REDUCED_MOTION } from "../../lib/useMediaQuery";
 
 // Shared horizontal rail — the one place the app's "row of cards you scroll sideways" lives, replacing
 // the hand-rolled `flex gap overflow-x-auto` strips (Cast / Related / collections) and the future
@@ -19,7 +20,7 @@ function scrollBehavior(): ScrollBehavior {
   const reduce =
     typeof window !== "undefined" &&
     typeof window.matchMedia === "function" &&
-    window.matchMedia("(prefers-reduced-motion: reduce)").matches;
+    window.matchMedia(REDUCED_MOTION).matches;
   return reduce ? "auto" : "smooth";
 }