[Vibranium][M1] Header: App menu integration

[Dosant]

Summary

Refine the app menu integration in the Chrome-Next header. The app menu is already rendering via ProjectNextAppMenu with fallback from chrome.getAppMenu$(). This issue covers polishing, DnD support, and strict enforcement.

Blocked by: #259107 (Header skeleton)

Scope

• Refine app menu rendering in the Chrome-Next header trailing actions area
• Enforce max 3 visible app-specific buttons (two secondary, one primary); rest overflow
• Buttons are text-color only (no primary/secondary color distinction)
• Verify fallback chain: config.appMenu -> chrome.getAppMenu$() -> undefined
• Integrate with Discover + Dashboard (partially done)
  • [Vibranium][M1] App Menu: Discover placement change #261913
• Coordinate with existing app menu feature flag to avoid doubled buttons
• Add architecture for global buttons (feedback button)
  • Feedback button in classic mode should stay in global header and it should NOT be a global item for app menu
  • In project mode the global header feedback button should NOT be visible and it should be a global item for app menu instead and it should be always shown, regardless if an app has any app menu items otherwise
• Add architecture for registering specific actions (e.g. "Add data" button)

Key files

• src/core/packages/chrome/browser-components/src/project_next/app_menu.tsx
• src/core/packages/chrome/browser-components/src/project_next/hooks/use_project_next_app_menu.ts
• src/core/packages/chrome/browser-components/src/project_next/trailing_actions.tsx
• src/core/packages/chrome/browser/src/next_header.ts (ChromeNextHeaderConfig.appMenu)

[elasticmachine]

Pinging @elastic/appex-sharedux (Team:SharedUX)