improvement(filters): count Source + Library scope as active; unify Clear all; add search clear (X)

The "Filters N active" badge and Clear all only tracked the sidebar facets
(tags/show/sort/content/date/channel), so the toolbar-level Source and the
Mine/Library scope neither bumped the count nor reset — inconsistent with
filtersToParams (which treats them as filters, so Save view/Share already
captured them).

- activeCount now includes Library scope and a non-default Source; "relevance"
  (auto-applied while searching, no manual option) is excluded from the sort
  count so typing a query no longer inflates the badge.
- Clear all resets scope back to "my" (Mine) and drops Source to organic,
  alongside the facets. The search q is intentionally preserved.
- The header search box gets a clear (X) button when it holds a value, so the
  search has its own reset (clearing it reverts the relevance sort to newest).

frontend/src/components/Header.tsx

@@ -1,5 +1,5 @@
 import { useTranslation } from "react-i18next";
-import { Library, Search, User, Youtube } from "lucide-react";
+import { Library, Search, User, X, Youtube } from "lucide-react";
 import type { FeedFilters, Me } from "../lib/api";
 import type { Page } from "../lib/urlState";
 import SyncStatus from "./SyncStatus";
@@ -81,8 +81,18 @@ export default function Header({
                 if (e.key === "Enter" && trimmedQ && canSearchYt) onYtSearch(trimmedQ);
               }}
               placeholder={t("header.searchPlaceholder")}
-              className="w-full bg-card border border-border rounded-full pl-9 pr-4 py-2 text-sm outline-none focus:border-accent"
+              className="w-full bg-card border border-border rounded-full pl-9 pr-9 py-2 text-sm outline-none focus:border-accent"
             />
+            {filters.q && (
+              <button
+                onClick={() => setFilters({ ...filters, q: "" })}
+                title={t("header.clearSearch")}
+                aria-label={t("header.clearSearch")}
+                className="absolute right-2.5 top-1/2 -translate-y-1/2 p-0.5 rounded-full text-muted hover:text-fg hover:bg-border/60 transition"
+              >
+                <X className="w-4 h-4" />
+              </button>
+            )}
           </div>
           {trimmedQ && canSearchYt && (
             <button

frontend/src/components/Sidebar.tsx

@@ -207,13 +207,23 @@ export default function Sidebar({
   const dateActive = !!filters.maxAgeDays || !!filters.dateFrom || !!filters.dateTo;
   const contentChanged =
     !filters.includeNormal || filters.includeShorts || filters.includeLive;
+  // Library (vs the default "my"/Mine) and a non-default provenance Source both narrow the feed,
+  // so they count as active filters too (Source only applies in Library scope). The header search
+  // `q` deliberately stays out — it has its own clear (✕) in the search box and isn't reset here.
+  const scopeActive = filters.scope === "all";
+  const sourceActive =
+    filters.scope === "all" && !!filters.librarySource && filters.librarySource !== "organic";
   const activeCount =
     filters.tags.length +
     (filters.show !== "unwatched" ? 1 : 0) +
-    (filters.sort !== "newest" ? 1 : 0) +
+    // "relevance" is auto-applied while searching (no manual dropdown option), so it's a search
+    // artifact, not a user-chosen sort filter — don't let typing a query inflate the count.
+    (filters.sort !== "newest" && filters.sort !== "relevance" ? 1 : 0) +
     (contentChanged ? 1 : 0) +
     (filters.channelId ? 1 : 0) +
-    (dateActive ? 1 : 0);
+    (dateActive ? 1 : 0) +
+    (scopeActive ? 1 : 0) +
+    (sourceActive ? 1 : 0);
   const active = activeCount > 0;
 
   async function shareView() {
@@ -227,7 +237,10 @@ export default function Sidebar({
 
   function clearAll() {
     setCustomDates(false);
-    setFilters({ ...DEFAULT_SIDEBAR_FILTERS, q: filters.q, scope: filters.scope });
+    // Reset every filter dimension to its default — including scope back to "my" (Mine) and the
+    // provenance Source (dropped with the rest, so it falls back to "organic"). The search `q` is
+    // intentionally preserved (it has its own ✕ in the search box).
+    setFilters({ ...DEFAULT_SIDEBAR_FILTERS, q: filters.q, scope: "my" });
   }
 
   const available: Record<WidgetId, boolean> = {

frontend/src/i18n/locales/de/header.json

@@ -1,6 +1,7 @@
 {
   "feed": "Feed",
   "searchPlaceholder": "Deine Abos durchsuchen…",
+  "clearSearch": "Suche löschen",
   "searchYoutube": "Auf YouTube suchen",
   "searchYoutubeTip": "Live auf YouTube nach diesem Begriff suchen (verbraucht gemeinsames API-Kontingent). Du kannst auch Enter drücken.",
   "channelManager": "Kanalverwaltung",

frontend/src/i18n/locales/en/header.json

@@ -1,6 +1,7 @@
 {
   "feed": "Feed",
   "searchPlaceholder": "Search your subscriptions…",
+  "clearSearch": "Clear search",
   "searchYoutube": "Search YouTube",
   "searchYoutubeTip": "Search live on YouTube for this term (uses shared API quota). You can also press Enter.",
   "channelManager": "Channel manager",

frontend/src/i18n/locales/hu/header.json

@@ -1,6 +1,7 @@
 {
   "feed": "Hírfolyam",
   "searchPlaceholder": "Keresés a feliratkozásaid között…",
+  "clearSearch": "Keresés törlése",
   "searchYoutube": "Keresés a YouTube-on",
   "searchYoutubeTip": "Élő keresés a YouTube-on erre a kifejezésre (a közös API-kvótát fogyasztja). Entert is nyomhatsz.",
   "channelManager": "Csatornakezelő",