Extensions: Remove checks for ViewType in BookmarkManagerPrivate API

This CL removes checks for a WebContents' ViewType in the
BookmarkManagerPrivate API to allow the side panel from using the
API as the panel's WebContents is part of top chrome, not from a
tab. The checks may from when kTabContents types were assumed to
access the native view [1].

[1] https://source.chromium.org/chromium/chromium/src/+/main:chrome/browser/extensions/api/bookmark_manager_private/bookmark_manager_private_api.cc;l=381;drf=chrome%2Fbrowser%2Fbookmarks%2Fbookmark_manager_extension_api.cc;drc=9d603396af7be1ccaab7f2843ff8c1dcca430538;bpv=1;bpt=0

Bug: 1234182
Change-Id: I44228adfb19fc6155e839aadf91dbb14cac08de6
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3098684
Reviewed-by: calamity <calamity@chromium.org>
Commit-Queue: John Lee <johntlee@chromium.org>
Cr-Commit-Position: refs/heads/master@{#912586}