[Mahi] Create MahiUiBrowserTest

This CL turns `MahiManagerImplTest` into an Ash browser test called
`MahiUiBrowserTest` because `MahiManagerImplTest` relies on a lot of
Ash features.

Bug: b/319731862, b/319735347
Change-Id: Ic9ba168c4d359e53038130830e155d94012d276b
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5416714


Reviewed-by: Xiyuan Xia <xiyuan@chromium.org>
Reviewed-by: Andre Le <leandre@chromium.org>
Commit-Queue: Andrew Xu <andrewxu@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1282776}