feat(app): refine session UI styling (#33860)

Co-authored-by: Brendan Allan <14191578+Brendonovich@users.noreply.github.com>

packages/app/src/pages/session/composer/session-composer-region.tsx

@@ -1,5 +1,6 @@
 import { Show, type JSX } from "solid-js"
 import { useLanguage } from "@/context/language"
+import { useSettings } from "@/context/settings"
 import { SessionPermissionDock } from "@/pages/session/composer/session-permission-dock"
 import { SessionQuestionDock } from "@/pages/session/composer/session-question-dock"
 import { SessionFollowupDock } from "@/pages/session/composer/session-followup-dock"
@@ -13,6 +14,7 @@ export function SessionComposerRegion(props: {
 }) {
   const language = useLanguage()
   const controller = props.controller
+  const settings = useSettings()
   const rolled = () => {
     const revert = controller.revert()
     return revert?.items.length ? revert : undefined
@@ -22,7 +24,11 @@ export function SessionComposerRegion(props: {
     <div
       ref={controller.setDockRef}
       data-component="session-prompt-dock"
-      class="w-full shrink-0 flex flex-col justify-center items-center pb-3 bg-background-stronger pointer-events-none"
+      classList={{
+        "w-full shrink-0 flex flex-col justify-center items-center pb-3 pointer-events-none": true,
+        "bg-v2-background-bg-base": settings.general.newLayoutDesigns(),
+        "bg-background-stronger": !settings.general.newLayoutDesigns(),
+      }}
     >
       <div
         classList={{