assistant: add new entry point eligibility check

- New entry point is available only for primary profile for now.

Bug: b:384781179
Test: unit_tests --gtest_filter=*AssistantBrowserDelegateImpl*
Change-Id: Ie0f8b9c4932db1d470334770fd505692ce43d2da
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6120152
Reviewed-by: Xiaohui Chen <xiaohuic@chromium.org>
Reviewed-by: Toni Barzic <tbarzic@google.com>
Reviewed-by: Matthew Mourgos <mmourgos@chromium.org>
Commit-Queue: Yuki Awano <yawano@google.com>
Cr-Commit-Position: refs/heads/main@{#1401607}