feat(ui): add 5-minute inactivity timeout to support page

Returns to idle screen after 5 minutes of no touch/scroll activity.
Timer resets on any pointer or scroll interaction.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

apps/machine/src/views/SupportView.vue

@@ -1,5 +1,5 @@
 <script setup lang="ts">
-import { ref, computed, onMounted } from 'vue'
+import { ref, computed, onMounted, onUnmounted } from 'vue'
 import { useRouter } from 'vue-router'
 import { nip19 } from 'nostr-tools'
 import { marked } from 'marked'
@@ -295,6 +295,27 @@ function isHiddenOnMobile(colIndex: number, totalCols: number): boolean {
 function goBack() {
   router.push('/')
 }
+
+// Inactivity timeout — return to idle after 5 minutes
+const SUPPORT_TIMEOUT = 5 * 60 * 1000
+let inactivityTimer: ReturnType<typeof setTimeout> | null = null
+
+function resetInactivityTimer() {
+  if (inactivityTimer) clearTimeout(inactivityTimer)
+  inactivityTimer = setTimeout(() => router.push('/'), SUPPORT_TIMEOUT)
+}
+
+onMounted(() => {
+  resetInactivityTimer()
+  document.addEventListener('pointerdown', resetInactivityTimer)
+  document.addEventListener('scroll', resetInactivityTimer, true)
+})
+
+onUnmounted(() => {
+  if (inactivityTimer) clearTimeout(inactivityTimer)
+  document.removeEventListener('pointerdown', resetInactivityTimer)
+  document.removeEventListener('scroll', resetInactivityTimer, true)
+})
 </script>
 
 <template>