Reland "kiosk: Migrate KioskEnterpriseInputApiBrowserTest to KioskMixin"

This relands commit ee87daf429ee8a4e40b6d757f8da56e98d54eaf3.

This fixes the flakiness in the original commit by waiting for the app
page navigation once in SetUpOnMainThread, instead of at every call to
SendMessageToExtension.

Original change's description:
> Revert "kiosk: Migrate KioskEnterpriseInputApiBrowserTest to KioskMixin"
>
> This reverts commit ee87daf429ee8a4e40b6d757f8da56e98d54eaf3.
>
> Reason for revert: Suspicious for causing flaky KioskEnterpriseInputApiBrowserTest failures on Linux ChromeOS builders
> i.e. https://ci.chromium.org/ui/p/chromium/builders/ci/Linux%20ChromiumOS%20MSan%20Tests/53964/overview
>
> Bug: 402454812
> Original change's description:
> > kiosk: Migrate KioskEnterpriseInputApiBrowserTest to KioskMixin
> >
> > Bug: 402454812
> > Test: testing/xvfb.py tools/autotest.py -C out_/Default chrome/browser/ash/login/app_mode/test/kiosk_enterprise_input_api_browsertest.cc
> > Change-Id: Ibed34cc9d724f87c4ae3bd1b438225b28cd64fbc
> > Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6695806
> > Reviewed-by: Ben Franz <bfranz@chromium.org>
> > Reviewed-by: Edman Anjos <edman@chromium.org>
> > Reviewed-by: Marc Treib <treib@chromium.org>
> > Commit-Queue: Edman Anjos <edman@chromium.org>
> > Cr-Commit-Position: refs/heads/main@{#1492985}
>
> Bug: 402454812
> No-Presubmit: true
> No-Tree-Checks: true
> No-Try: true
> Change-Id: Ibf57d8c65e60f8483dc49f0ba48c72c928068513
> Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6797251
> Owners-Override: Nidhi Jaju <nidhijaju@chromium.org>
> Auto-Submit: Nidhi Jaju <nidhijaju@chromium.org>
> Commit-Queue: Rubber Stamper <rubber-stamper@appspot.gserviceaccount.com>
> Bot-Commit: Rubber Stamper <rubber-stamper@appspot.gserviceaccount.com>
> Cr-Commit-Position: refs/heads/main@{#1493360}

Bug: 402454812
Change-Id: Idfddcc769c9deb24c75cd58a7de963f6c554eb5a
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6798046
Reviewed-by: Marc Treib <treib@chromium.org>
Commit-Queue: Edman Anjos <edman@chromium.org>
Reviewed-by: Ben Franz <bfranz@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1494082}