Make cutout dark are in tab switcher in landscape and draw content behind the gesture nav bar in tab switcher

[catalinradoiu]

Task/Issue URL:https://app.asana.com/1/137249556945/project/1211724162604201/task/1215854420455811?focus=true
Tech Design URL (if applicable):

Description

Moves the updateLayoutForDisplayCutout method from BrowserActivity and CustomTabActivity into the base DuckDuckGoActivity class, making it reusable across all activities. This method is now also called in TabSwitcherActivity to properly handle display cutout behavior during orientation changes.

Additionally, navigation bar insets are now applied to the navigation bar mockup in BrowserActivity, and the tab switcher's navigation bar insets are configured to draw behind gesture navigation.

Steps to test this PR

Display Cutout Handling

• On a device with a display cutout (notch), rotate to landscape and verify the content does not extend into the cutout area in BrowserActivity, CustomTabActivity, and TabSwitcherActivity
• Rotate back to portrait and verify the layout returns to default cutout behavior

Navigation Bar Insets

• Verify the navigation bar mockup in BrowserActivity is correctly inset (when launching the app in split omnibar mode)
• In TabSwitcherActivity, verify the tab list draws correctly behind the gesture navigation bar

UI changes

Before	After
!(Upload before screenshot)	(Upload after screenshot)

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Note

Low Risk
Changes are limited to window layout flags and edge-to-edge padding on browser, custom tab, and tab switcher screens; no data or security paths are touched.

Overview
Display cutout: updateLayoutForDisplayCutout moves from duplicated code in BrowserActivity and CustomTabActivity into DuckDuckGoActivity. In landscape it sets LAYOUT_IN_DISPLAY_CUTOUT_MODE_NEVER so content stays out of the notch/cutout; portrait keeps default behavior. TabSwitcherActivity now calls this on create (when browser edge-to-edge is on), matching browser/custom-tab handling on rotation.

Navigation bar insets: With edge-to-edge in BrowserActivity, navigation bar insets are applied to navigationBarMockup (split omnibar startup mockup). In TabSwitcherActivity for top omnibar, applyNavigationBarInsets on the tabs container uses drawBehindGestureNav = true so the tab grid can extend behind the gesture navigation bar instead of stopping above it.

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[catalinradoiu]

• Make cutout dark are in tab switcher in landscape and draw content behind the gesture nav bar in tab switcher #8933 👈 (View in Graphite)
• develop

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