Move search bar background protection on top of scrollbar.

This way the search bar looks more connected to the keyboard
without the scrollbar showing next to it.

Note: Here the search bar is added on top of all other views
(previously it was inserted above only the header), and the
protection is always added just behind the search bar.

Also adjusts the height of the scrollbar to end above the search
bar when floating search bar is enabled.

Screenshots:
Scrollbar behind search bar: https://drive.google.com/file/d/10ZJ-q5nA9ZBjr7gjoauTDDAbQRUNk7S7/view?usp=share_link&resourcekey=0-pF6eOcuKz2_sCA_eZpa1Sw
New scrollbar height with floating search: https://drive.google.com/file/d/1fVIJjiG7RMme5fBXiSJmxNfOhHJ__Gwj/view?usp=share_link&resourcekey=0-b9RsB7f55U_rIZBu4IhVGQ

Fix: 265478433
Test: With and without floating search and always-on keyboard and
work profile.

Change-Id: I4f7ae0d376dae215c0cbd8deaee3e4a409d21ae4