feat: add scroll to bottom button and auto-scroll on session load

src/pages/GamePage.css

@@ -225,6 +225,33 @@
   display: flex;
   flex-direction: column;
   overflow: hidden;
+  position: relative;
+}
+
+.scroll-to-bottom-btn {
+  position: absolute;
+  bottom: 5rem;
+  right: 1rem;
+  width: 40px;
+  height: 40px;
+  background: rgba(30, 30, 30, 0.9);
+  border: 1px solid rgba(255, 255, 255, 0.15);
+  border-radius: 50%;
+  color: #fff;
+  font-size: 1.25rem;
+  cursor: pointer;
+  display: flex;
+  align-items: center;
+  justify-content: center;
+  z-index: 5;
+  transition: all 0.2s;
+  backdrop-filter: blur(8px);
+  -webkit-backdrop-filter: blur(8px);
+}
+
+.scroll-to-bottom-btn:hover {
+  background: rgba(50, 50, 50, 0.95);
+  transform: scale(1.05);
 }
 
 .messages-container {
@@ -629,4 +656,12 @@
     right: 0;
     left: auto;
   }
+
+  .scroll-to-bottom-btn {
+    width: 36px;
+    height: 36px;
+    bottom: 4.5rem;
+    right: 0.75rem;
+    font-size: 1rem;
+  }
 }