feat: implement server password login, YouTube source, and improved bot selector UI

- **TS server password** (#7/#9): add serverPassword field across database,
  manager, bot API, and Settings UI — allows joining password-protected servers
- **YouTube audio source** (#1/#10): new YouTubeProvider using yt-dlp binary;
  adds -y flag in chat commands, /api/music supports platform=youtube,
  YouTube badge in SongCard, yt-dlp-wrap npm dependency
- **Bot selector UI** (#14): selector always visible (not just when >1 bot),
  bigger button with border and play-state indicator; per-bot URL routing at
  /bot/:id with BotRedirect view; copy-link button in dropdown

Closes #1, #7, #9, #10, #14

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/data/database.test.ts

@@ -62,6 +62,7 @@ describe("database", () => {
       autoStart: true,
       serverProtocol: "",
       ts6ApiKey: "",
+      serverPassword: "",
     };
 
     botDb.saveBotInstance(instance);
@@ -90,6 +91,7 @@ describe("database", () => {
       autoStart: false,
       serverProtocol: "",
       ts6ApiKey: "",
+      serverPassword: "",
     });
 
     expect(botDb.deleteBotInstance("bot1")).toBe(true);