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