refactor(feed): drive the feed sort toolbar through the shared SortControl (R13 S1)

The feed's bespoke select + asc/desc button is now the generic SortControl,
fed a SortOption[] built from the feed vocabulary (relevance offered only with
a query; shuffle/relevance directionless). The feedSort wire codec
(parseSort/buildSort) stays as the server-boundary translation, and the
reshuffle button rides SortControl's `trailing` slot so shuffle keeps its
re-seed affordance. Behaviour-equivalent; ArrowUp/ArrowDown imports dropped.

frontend/src/components/Feed.tsx

@@ -8,8 +8,6 @@ import {
 } from "@tanstack/react-query";
 import { qk } from "../lib/queryKeys";
 import {
-  ArrowDown,
-  ArrowUp,
   ArrowLeft,
   Columns2,
   Grid3x3,
@@ -34,12 +32,14 @@ import {
   SORT_KEYS,
   type SortKey,
 } from "../lib/feedSort";
+import { type SortOption } from "../lib/columnSort";
 import { FEED_VIEWS, type FeedView } from "../lib/feedView";
 import { clearedFilters, useActiveFilters } from "../lib/useActiveFilters";
 import ActiveFilterChips from "./ActiveFilterChips";
 import { LoadingState, StateMessage } from "./QueryState";
 import { PageToolbar } from "./PageShell";
 import { useWizard } from "./WizardProvider";
+import SortControl from "./SortControl";
 import ViewSwitcher from "./ViewSwitcher";
 import VirtualFeed from "./VirtualFeed";
 // Lazy: the in-app YouTube player (IFrame API) loads only when a video is first opened.
@@ -547,6 +547,18 @@ export default function Feed({
     );
 
   const { key: sortKey, dir: sortDir } = parseSort(filters.sort);
+  // The feed's sort vocabulary as source-agnostic options for the shared SortControl. Relevance only
+  // ranks meaningfully with a search term (offered then); shuffle/relevance are directionless.
+  const sortOptions: SortOption[] = (
+    filters.q.trim() ? (["relevance", ...sortKeys] as SortKey[]) : sortKeys
+  ).map((k) => ({
+    key: k,
+    label: t("feed.sortKey." + k),
+    directionless: DIRECTIONLESS.includes(k),
+    defaultDir: DIRECTIONLESS.includes(k)
+      ? undefined
+      : SORT_DEFAULT_DIR[k as Exclude<SortKey, "shuffle" | "relevance">],
+  }));
 
   const toolbar = (
     <div className="pb-3">
@@ -615,58 +627,33 @@ export default function Feed({
         </span>
         <div className="ml-auto flex items-center gap-2">
           <span className="text-xs text-muted">{t("feed.sortLabel")}</span>
-          <select
-            value={sortKey}
-            onChange={(e) => {
-              const key = e.target.value as SortKey;
-              const dir = DIRECTIONLESS.includes(key)
-                ? "desc"
-                : SORT_DEFAULT_DIR[key as Exclude<SortKey, "shuffle" | "relevance">];
+          <SortControl
+            options={sortOptions}
+            sort={{ key: sortKey, dir: sortDir }}
+            onChange={(next) => {
+              if (!next) return; // the feed is always sorted — no "no sort" option is offered
               setFilters({
                 ...filters,
-                sort: buildSort(key, dir),
-                seed: key === "shuffle" ? rollSeed() : undefined,
+                sort: buildSort(next.key as SortKey, next.dir),
+                seed: next.key === "shuffle" ? rollSeed() : undefined,
               });
             }}
-            aria-label={t("feed.sortLabel")}
-            className="bg-surface border border-border rounded-lg px-2 py-1.5 text-sm focus:outline-hidden focus:ring-2 focus:ring-accent/40"
-          >
-            {/* Relevance only ranks meaningfully when there's a search term — offer it then. */}
-            {(filters.q.trim() ? (["relevance", ...sortKeys] as SortKey[]) : sortKeys).map((k) => (
-              <option key={k} value={k}>
-                {t("feed.sortKey." + k)}
-              </option>
-            ))}
-          </select>
-          {!DIRECTIONLESS.includes(sortKey) && (
-            <button
-              onClick={() =>
-                setFilters({
-                  ...filters,
-                  sort: buildSort(sortKey, sortDir === "asc" ? "desc" : "asc"),
-                })
-              }
-              title={sortDir === "asc" ? t("feed.dirAsc") : t("feed.dirDesc")}
-              aria-label={sortDir === "asc" ? t("feed.dirAsc") : t("feed.dirDesc")}
-              className="shrink-0 p-1.5 rounded-lg border border-border bg-card text-fg hover:border-accent hover:text-accent active:translate-y-px transition"
-            >
-              {sortDir === "asc" ? (
-                <ArrowUp className="w-4 h-4" />
-              ) : (
-                <ArrowDown className="w-4 h-4" />
-              )}
-            </button>
-          )}
-          {sortKey === "shuffle" && (
-            <button
-              onClick={() => setFilters({ ...filters, seed: rollSeed() })}
-              title={t("sidebar.reshuffle")}
-              aria-label={t("sidebar.reshuffle")}
-              className="shrink-0 p-1.5 rounded-lg border border-border bg-card text-fg hover:border-accent hover:text-accent active:translate-y-px transition"
-            >
-              <RefreshCw className="w-4 h-4" />
-            </button>
-          )}
+            label={t("feed.sortLabel")}
+            ascLabel={t("feed.dirAsc")}
+            descLabel={t("feed.dirDesc")}
+            trailing={
+              sortKey === "shuffle" ? (
+                <button
+                  onClick={() => setFilters({ ...filters, seed: rollSeed() })}
+                  title={t("sidebar.reshuffle")}
+                  aria-label={t("sidebar.reshuffle")}
+                  className="shrink-0 p-1.5 rounded-lg border border-border bg-card text-fg hover:border-accent hover:text-accent active:translate-y-px transition"
+                >
+                  <RefreshCw className="w-4 h-4" />
+                </button>
+              ) : undefined
+            }
+          />
           <span className="mx-0.5 h-5 w-px bg-border" aria-hidden="true" />
           <ViewSwitcher
             value={view}