Suppress screen-orientation lock/unlock when entering/leaving PiP - #37848

Resolves brave/brave-browser#56784

Entering or leaving the Brave managed YouTube Picture-in-Picture window briefly rotated the system UI and the video to landscape on phones. This PR restores the orientation suppression that #30578 introduced and that later regressed, and hardens the mechanism so it cannot silently break the same way again.

Phone only. Not reproducible on tablet.

Root cause

The flash is suppressed by BraveScreenOrientationDelegateAndroid, which skips the screen orientation lock/unlock while a fullscreen request is armed on the current NavigationEntry. That state is written in the browser layer (the YouTube PiP tab helper) and read in the content layer (the delegate). Two independent problems broke the link:

1. Disconnected state. PR Fix YouTube PiP script injection after navigation #37366 reworked the tab helper to track the request under a private key on the NavigationEntry and stopped writing the shared state the delegate reads. Nothing wrote what the delegate read, so the suppression never triggered.

2. Key identity across components. The shared key was a header defined inline constexpr array. SupportsUserData matches keys by pointer address, not by string value, and a header defined key can resolve to a different address in each component. The browser layer writer and the content layer reader ended up with different addresses, so GetUserData missed even once the state was reconnected. This is the failure mode Chromium documents at crbug.com/589840.

Both were confirmed on device: the delegate read the same NavigationEntry the tab helper wrote, yet found no data, because the two sides used different key addresses.

Fix

Expose the per entry fullscreen flag through exported accessor functions in content/public, and keep the SupportsUserData key a single file local definition. The two layers now call functions instead of sharing a key, so the address mismatch is impossible by construction.

• New content/public/browser/navigation_entry_fullscreen.{h,cc} with SetNavigationEntryFullscreenRequested and IsNavigationEntryFullscreenRequested, backed by a file local presence key.
• The delegate reads through IsNavigationEntryFullscreenRequested.
• The YouTube PiP tab helper writes through SetNavigationEntryFullscreenRequested.
• Removed the previous fullscreen_page_data.h (exported struct plus exported key).

This follows the pattern content/public uses for other cross layer predicates (for example IsIsolatedContext) and the key handling Chromium documents for WebContentsUserData.

Test plan

Phone only; not reproducible on tablet.

1. Open m.youtube.com and play a video.
2. Enter PiP. The system UI and video must not rotate to landscape.
3. Expand back to the browser view. Again no landscape rotation.
4. Repeat the cycle a few times.
5. Observe no flash entering or leaving PiP in either direction.

Notes for reviewers

• Boolean cross layer state is exposed as free functions rather than an exported UserData key on purpose. The key must be one address across the browser and content components; a single file local definition guarantees that, while a header inline key does not.
• brave/content/public/browser/DEPS gains +content/public/browser so the new .cc can include navigation_entry.h and reach NavigationEntry's SupportsUserData methods. This matches the sibling content/browser/screen_orientation/DEPS.
• No automated test is added: the path is Android only, cross layer, and driven by the renderer entering fullscreen, so it is not practical to unit test. This is consistent with the original Fix Picture-in-Picture orientation issues for YouTube videos #30578.