[VC] split SeaPenProvider into base and impl.

(1) PersonalizationAppSeaPenProviderImpl is splitted into
    PersonalizationAppSeaPenProviderBase and
    PersonalizationAppSeaPenProviderImpl. We have to do this under
    chrome/browser/ash because of browser objects accessing.

(2) VcBackgroundSeaPenProviderImpl is also added for the
    implementation of VcBackground.

(3) Tests are added accordingly.

Bug=b/308498859
TEST="autoninja -C out/Test chrome/test:browser_tests && out/Test/browser_tests --gtest_filter=VcBackgroundSeaPenProviderImplTest.*"

Low-Coverage-Reason: LARGE_SCALE_REFACTOR

Change-Id: I8edbba5bd2bf1bdd885205b36904ac1acfc37ccb
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5167208
Reviewed-by: Jeffrey Young <cowmoo@google.com>
Reviewed-by: Sam McNally <sammc@chromium.org>
Commit-Queue: Charles Zhao <charleszhao@chromium.org>
Reviewed-by: CJ Huang <chenjih@google.com>
Cr-Commit-Position: refs/heads/main@{#1245662}