fix(spotify): PATH-aware binary presence detection (bin/ or PATH) [whole-branch I3,m1]

rustPresent/goPresent and getBackendInfo used existsSync(findX()), which for a
bare PATH command name resolves against cwd, not $PATH — so a scoop/choco/cargo/
apt install was invisible and Spotify was gated off. Add a sync PATH-aware
resolveExecutable() + isLibrespotPresent()/isGoLibrespotPresent() in binary.ts
and route controller.ts and web/server.ts through them.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

src/music/spotify/controller.ts

@@ -15,12 +15,7 @@ import type {
   SpotifyTrackEndedEvent,
   SpotifyNowPlaying,
 } from "./backend.js";
-import {
-  isGoLibrespotSupported,
-  findGoLibrespot,
-  isRustLibrespotSupported,
-  findLibrespot,
-} from "./binary.js";
+import { isGoLibrespotPresent, isLibrespotPresent } from "./binary.js";
 import { GoLibrespotBackend } from "./go-librespot.js";
 import { RustLibrespotBackend } from "./rust-librespot.js";
 import {
@@ -151,11 +146,13 @@ export class SpotifyController extends EventEmitter {
   }
 
   private goPresent(): boolean {
-    return isGoLibrespotSupported() && existsSync(findGoLibrespot());
+    // PATH-aware, sync presence gate (Bug I3): a bare PATH-installed binary is
+    // resolved against $PATH, not existsSync()'d against process.cwd().
+    return isGoLibrespotPresent();
   }
 
   private rustPresent(): boolean {
-    return isRustLibrespotSupported() && existsSync(findLibrespot());
+    return isLibrespotPresent();
   }
 
   /**