feat(web): library homepage, chain in settings

Implements the §9.7 shell rulings (issue #173): "/" renders the library
and the board route is gone — every former board target (Esc, cleared
search, detail parent routes, the not-found fallback) lands on the
library. The signal chain moves into /settings as its first section,
lamps still driven by the health poll; the master lamp stays on the
rail. The wordmark is now a real anchor that navigates home.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

web/src/router.ts

@@ -3,7 +3,6 @@
 // state passed to pushState, so a manually edited or copy-pasted URL works.
 
 export type Route =
-  | { kind: "board" }
   | { kind: "library" }
   | { kind: "queues" }
   | { kind: "settings" }
@@ -16,9 +15,6 @@ export type Route =
 
 export function parseRoute(url: URL): Route {
   const segments = url.pathname.split("/").filter(Boolean);
-  if (segments.length === 1 && segments[0] === "library") {
-    return { kind: "library" };
-  }
   if (segments.length === 1 && segments[0] === "queues") {
     return { kind: "queues" };
   }
@@ -27,7 +23,7 @@ export function parseRoute(url: URL): Route {
   }
   if (segments.length === 1 && segments[0] === "search") {
     const query = url.searchParams.get("q") ?? "";
-    return query === "" ? { kind: "board" } : { kind: "search", query };
+    return query === "" ? { kind: "library" } : { kind: "search", query };
   }
   if (segments.length === 2 && segments[0] === "movies") {
     const movieId = Number(segments[1]);
@@ -70,15 +66,14 @@ export function parseRoute(url: URL): Route {
       return { kind: "episodeReleases", episodeId };
     }
   }
-  return { kind: "board" };
+  // §9.7: the library is the homepage — "/" and every unrecognised path land here
+  return { kind: "library" };
 }
 
 export function routePath(route: Route): string {
   switch (route.kind) {
-    case "board":
-      return "/";
     case "library":
-      return "/library";
+      return "/";
     case "queues":
       return "/queues";
     case "settings":