fix(web): pin chat input and make session list scrollable independently

Constrain the main layout to viewport height (h-dvh) and override
SidebarProvider's min-h-svh so the height chain propagates correctly.
Change main-container overflow from auto to hidden so the outer
container never scrolls. Use absolute-positioning pattern for
session sidebar ScrollArea (matching chat messages pattern) to
ensure sessions scroll independently while the chat input stays fixed.

apps/web/src/components/main-container/index.vue

@@ -1,6 +1,6 @@
 <template>
   <SidebarInset class="flex flex-col overflow-hidden">
-    <section class="flex-1 overflow-y-auto">
+    <section class="flex-1 min-h-0 overflow-hidden">
       <router-view v-slot="{ Component }">
         <KeepAlive>
           <component :is="Component" />

apps/web/src/layout/main-layout/index.vue

@@ -1,6 +1,7 @@
 <template>
-  <section class="flex">
+  <section class="flex h-dvh overflow-hidden">
     <sidebar-provider
+      class="min-h-0 h-full"
       :default-open="sidebarDefaultOpen"
     >
       <section class="relative">

apps/web/src/pages/home/components/session-sidebar.vue

@@ -100,8 +100,10 @@
       </DropdownMenu>
     </div>
 
-    <ScrollArea class="flex-1">
-      <div class="flex flex-col gap-1 px-1.5 overflow-hidden">
+    <div class="flex-1 relative min-h-0">
+      <div class="absolute inset-0">
+        <ScrollArea class="h-full">
+          <div class="flex flex-col gap-1 px-1.5">
             <SessionItem
               v-for="session in filteredSessions"
               :key="session.id"
@@ -129,6 +131,8 @@
           </div>
         </ScrollArea>
       </div>
+    </div>
+  </div>
 </template>
 
 <script setup lang="ts">