feat(ui): add scroll-to-latest button in assistant feed

Track the assistant feed scroll position and footer height, and show a
floating button to jump back to the newest message when scrolled up.

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

frontend/src/ui/styles.css

@@ -3602,6 +3602,11 @@ button:disabled {
   font-size: 13px;
 }
 
+.assistant-footer-dock {
+  width: 100%;
+  flex: 0 0 auto;
+}
+
 .assistant-feed {
   position: relative;
   width: 100%;
@@ -3637,6 +3642,40 @@ button:disabled {
   background: #dfe0e2;
 }
 
+.assistant-scroll-to-end {
+  position: absolute;
+  inset-inline: 0;
+  z-index: 12;
+  display: flex;
+  justify-content: center;
+  pointer-events: none;
+}
+
+.assistant-scroll-to-end button {
+  width: 40px;
+  height: 40px;
+  display: grid;
+  place-items: center;
+  border: 1px solid #e1e3e8;
+  border-radius: 999px;
+  color: #373b42;
+  background: #fff;
+  box-shadow: 0 8px 24px rgba(17, 24, 39, 0.12);
+  pointer-events: auto;
+  transition: background 0.15s ease, border-color 0.15s ease, transform 0.15s ease;
+}
+
+.assistant-scroll-to-end button:hover {
+  border-color: #d4d8df;
+  background: #f8f9fa;
+  transform: translateY(-1px);
+}
+
+.assistant-scroll-to-end button:active {
+  background: #eef0f3;
+  transform: translateY(0);
+}
+
 .generated-preview-card {
   display: grid;
   gap: 10px;