quick-answers: wire design selection value

- Pick an expected design selection based on flags, etc.
- This CL also flips the default value of kQuickAnswersMaterialNextUI.

Bug: b:340628664
Test: manually tested
Change-Id: I9e327a01ed40af9b8a9338335f5529b094284956
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5824220


Commit-Queue: Yuki Awano <yawano@google.com>
Reviewed-by: Xiaohui Chen <xiaohuic@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1349507}