test: 38 layout mode tests + fix half/full/float CSS positioning

- Fix side panel and full screen not covering full viewport
- Fix floating mode initial position (near chat button, not top-right)
- Reset width/height inline styles when switching modes
- Add 84-chat-layout-modes.test.mjs: 38 assertions covering
  compact, side panel, full screen, floating, drag, rapid switching,
  and user avatar rendering

static/css/04-interactive/_chat.css

@@ -88,6 +88,7 @@
     bottom: 0;
     left: auto;
     width: 50vw;
+    height: auto;
     max-height: none;
     border-radius: 0;
     border-left: 2px solid var(--border-light);
@@ -98,14 +99,17 @@
     flex: 1;
 }
 
-/* Size: Floating — draggable, resizable feel */
+/* Size: Floating — draggable, resizable window */
 .chat-panel.chat-float {
-    top: 10vh;
-    left: auto;
+    bottom: 10.5rem;
     right: 2rem;
-    bottom: auto;
+    top: auto;
+    left: auto;
     width: 420px;
+    height: 450px;
     max-height: 70vh;
+    min-width: 300px;
+    min-height: 250px;
     border-radius: 8px;
     box-shadow: 0 8px 32px rgba(0, 0, 0, 0.3);
     resize: both;
@@ -124,13 +128,14 @@
     flex: 1;
 }
 
-/* Size: Full width */
+/* Size: Full screen */
 .chat-panel.chat-full {
     top: 0;
     left: 0;
     right: 0;
     bottom: 0;
     width: 100%;
+    height: auto;
     max-height: none;
     border-radius: 0;
     border: none;