Improve mobile conversation drawer layering and empty state (#59) (#60)

## Summary
- Closes #59
- Mobile conversation drawer is now a fixed sheet with stronger stacking over dashboard content
- Adds explicit close (X) control and empty-state copy when there are no conversations
- Keeps existing close-on-select / New Chat behavior

## Test plan
- [ ] Mobile: open Conversations drawer — sheet + overlay appear above content
- [ ] Tap X or overlay — drawer closes
- [ ] Empty conversation list shows guidance text
- [ ] Select conversation / New Chat closes drawer and chat still works
- [ ] Desktop sidebar layout unchangedReviewed-on: #60

llm-fe/src/llm-fe/pages/AsyncDashboard2/AsyncDashboard2.tsx

@@ -2,7 +2,7 @@ import React, { useContext, useEffect, useRef, useState } from "react";
 import styled, { ThemeContext } from "styled-components";
 import { Formik, Form, Field } from "formik";
 import * as Yup from "yup";
-import { AttachFile, Delete, Send, Menu } from "@mui/icons-material"; // Keeping icons for now, can replace later if needed
+import { AttachFile, Delete, Send, Menu, Close } from "@mui/icons-material"; // Keeping icons for now, can replace later if needed
 import { Tooltip } from "@mui/material";
 import Markdown from "markdown-to-jsx";
 
@@ -44,10 +44,15 @@ const Sidebar = styled.div<{ $isOpen: boolean }>`
   transition: transform 0.3s ease;
 
   @media (max-width: 768px) {
-    position: absolute;
+    position: fixed;
+    top: 0;
+    left: 0;
+    width: min(85vw, 320px);
+    height: 100vh;
     transform: ${({ $isOpen }) => $isOpen ? 'translateX(0)' : 'translateX(-100%)'};
     background: ${({ theme }) => theme.darkMode ? 'rgba(0, 0, 0, 0.95)' : 'rgba(255, 255, 255, 0.95)'};
     box-shadow: ${({ $isOpen }) => $isOpen ? '0 0 20px rgba(0,0,0,0.5)' : 'none'};
+    z-index: 120;
   }
 `;
 
@@ -88,7 +93,7 @@ const Overlay = styled.div<{ $isOpen: boolean }>`
   height: 100vh;
   background: rgba(0, 0, 0, 0.5);
   backdrop-filter: blur(2px);
-  z-index: 15;
+  z-index: 110;
   opacity: ${({ $isOpen }) => $isOpen ? 1 : 0};
   pointer-events: ${({ $isOpen }) => $isOpen ? 'auto' : 'none'};
   transition: opacity 0.3s ease;
@@ -98,6 +103,36 @@ const Overlay = styled.div<{ $isOpen: boolean }>`
   }
 `;
 
+const MobileSidebarHeader = styled.div`
+  display: none;
+
+  @media (max-width: 768px) {
+    display: flex;
+    align-items: center;
+    justify-content: space-between;
+    margin-bottom: 1rem;
+    color: ${({ theme }) => theme.colors.text};
+    font-weight: 700;
+    font-size: 1rem;
+  }
+`;
+
+const MobileSidebarCloseButton = styled.button`
+  display: none;
+
+  @media (max-width: 768px) {
+    display: flex;
+    align-items: center;
+    justify-content: center;
+    border: none;
+    background: transparent;
+    color: ${({ theme }) => theme.colors.text};
+    cursor: pointer;
+    border-radius: 999px;
+    padding: 0.3rem;
+  }
+`;
+
 const MainContent = styled.div`
   flex: 1;
   height: 100%;
@@ -384,6 +419,12 @@ const AsyncDashboardInner = (): JSX.Element => {
       </MobileSidebarToggle>
 
       <Sidebar $isOpen={isSidebarOpen}>
+        <MobileSidebarHeader>
+          <span>Conversations</span>
+          <MobileSidebarCloseButton onClick={() => setIsSidebarOpen(false)} aria-label="Close conversations drawer">
+            <Close fontSize="small" />
+          </MobileSidebarCloseButton>
+        </MobileSidebarHeader>
         <NewChatButton onClick={() => {
           setSelectedConversation(undefined);
           setIsSidebarOpen(false);
@@ -391,7 +432,17 @@ const AsyncDashboardInner = (): JSX.Element => {
           + New Chat
         </NewChatButton>
         <div style={{ overflowY: 'auto', flex: 1 }}>
-          {conversations.map((convo) => (
+          {conversations.length === 0 ? (
+            <div style={{
+              color: theme?.darkMode ? 'rgba(255,255,255,0.55)' : 'rgba(0,0,0,0.55)',
+              fontSize: '0.9rem',
+              lineHeight: 1.5,
+              padding: '0.25rem 0.5rem'
+            }}>
+              No conversations yet. Start with <strong>+ New Chat</strong>.
+            </div>
+          ) : (
+            conversations.map((convo) => (
               <ConversationItem
                 key={convo.id}
                 $active={convo.id === selectedConversation}
@@ -414,7 +465,8 @@ const AsyncDashboardInner = (): JSX.Element => {
                   </IconButton>
                 )}
               </ConversationItem>
-          ))}
+            ))
+          )}
         </div>
       </Sidebar>