fix(profile): apply custom avatar immediately on idle setCustomAvatar / connect

Review feedback on PR #56:

1. setCustomAvatar(buf) now triggers applyIdleAvatar when the bot is idle
   (currentSong=null OR avatarEnabled=false). Spec said this; original impl
   only stored the buffer, so a fresh upload from Settings was invisible
   until next stop event. Track currentSong in BotProfileManager for the
   idle check.

2. onConnect drops the !avatarEnabled guard — on a fresh connect there's
   no song playing yet, so the spec matrix wants the custom avatar shown
   regardless of sync. Previously bots reconnected with a stale TS3
   server-side avatar.

3. CustomAvatarRow: defer the initializing=false flip to nextTick so the
   load-time data-url assignment's queued watcher sees initializing=true
   and bails. Removes the redundant PUT-on-mount that echoed the just-
   loaded bytes back to the server.

4. BotInstance avatar load wrapped in try/catch — a corrupt/locked file
   no longer crashes startup; we log and continue with no custom avatar.

Tests rewritten: 10 cases covering the full behavior matrix
(idle vs playing × sync on/off × custom set/null × stop/connect).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

web/src/components/CustomAvatarRow.vue

@@ -3,12 +3,15 @@
 </template>
 
 <script setup lang="ts">
-import { ref, onMounted, watch } from 'vue';
+import { ref, onMounted, watch, nextTick } from 'vue';
 import axios from 'axios';
 import AvatarUpload from './AvatarUpload.vue';
 
 const props = defineProps<{ botId: string }>();
 const avatarDataUrl = ref<string | null>(null);
+// Stays true until the watcher queued by the load-time assignment has run,
+// so the initial null → loaded-data-url transition does not fire a redundant
+// PUT echoing the just-fetched bytes back to the server.
 let initializing = true;
 
 async function loadCurrent() {
@@ -22,6 +25,9 @@ async function loadCurrent() {
     }
     avatarDataUrl.value = null;
   } finally {
+    // Wait for the watcher's flush queue to drain (it'll see initializing=true
+    // and bail), then release for real user-driven changes.
+    await nextTick();
     initializing = false;
   }
 }