fix(nav): a search the address opened marks its entry, so a channel over it keeps it

A search reached by a reload or a link had no _yt mark on its entry, so a channel opened from its
results carried none, and a landing back on that channel (an overlay over it closing) ended the
search under it.

frontend/src/features/navigation/NavigationProvider.tsx

@@ -296,9 +296,10 @@ export function NavigationProvider({ children }: { children: ReactNode }) {
   // then sync state from history.state on popstate — the browser restores each entry's URL for us, so
   // the popstate handler only needs to read history.state.
   useEffect(() => {
-    // The entry's `_yt` mark stays while the address still names its search (a reload of it); a mark
-    // left without one (an older build's entry) goes. _chan/_chanName are always kept so a channel
-    // page survives F5.
+    // The entry of a search the address names carries its `_yt` mark, whichever way it opened (sent
+    // from the box, a reload, a link): a channel opened from its results reads the search under it
+    // from that mark. A mark left without one (an older build's entry) goes. _chan/_chanName are
+    // always kept so a channel page survives F5.
     const st = window.history.state || {};
     // Mirror the resolved initial page to the address bar (the feed too) so a page reached from the
     // stored landing pref — not just from the URL — is itself bookmarkable. urlWithParams keeps the
@@ -316,8 +317,10 @@ export function NavigationProvider({ children }: { children: ReactNode }) {
       ...retiredParams(linked ?? (resolvePage(remembered) === mountPage ? remembered : null)),
       page: mountPage,
     });
-    if (st._yt && ytSearchFrom(new URLSearchParams(window.location.search)) != null) {
-      window.history.replaceState({ ...st, sfPage: mountPage }, "", url);
+    const named =
+      mountPage === "feed" ? ytSearchFrom(new URLSearchParams(window.location.search)) : null;
+    if (named != null) {
+      window.history.replaceState({ ...st, _yt: named, sfPage: mountPage }, "", url);
     } else {
       const { _yt: _staleYt, _ytScrape: _staleScrape, ...rest } = st;
       window.history.replaceState({ ...rest, sfPage: mountPage }, "", url);

frontend/src/features/navigation/NavigationProvider.ytSearch.dom.test.tsx

@@ -138,6 +138,12 @@ describe("NavigationProvider · the YouTube search in the address", () => {
     expect(window.history.state?._yt).toBe("lofi");
   });
 
+  it("marks the entry of a search the address opened (a reload, a link)", () => {
+    window.history.replaceState({ sfPage: "feed" }, "", "/?page=feed&yt=lofi");
+    render();
+    expect(window.history.state?._yt).toBe("lofi");
+  });
+
   it("drops an older build's search mark the address does not name", () => {
     window.history.replaceState(
       { sfPage: "feed", _yt: "lofi", _ytScrape: true },
@@ -255,6 +261,16 @@ describe("NavigationProvider · the YouTube search in the address", () => {
     expect(result.current.ytSearchAsked).toBe(true);
   });
 
+  it("a landing on a channel opened from a search the address opened keeps the search", () => {
+    window.history.replaceState({ sfPage: "feed" }, "", "/?page=feed&yt=lofi");
+    const { result } = render();
+    act(() => result.current.openChannel("UC1"));
+    act(() => {
+      window.dispatchEvent(new PopStateEvent("popstate", { state: window.history.state }));
+    });
+    expect(result.current.ytSearch).toBe("lofi");
+  });
+
   it("a channel closed in place over the search names the search again", () => {
     const { result } = render();
     act(() => result.current.enterYtSearch("lofi"));