e2e(specs): startup, menu bar, tray, and notification Playwright specs

[yasserfaraazkhan]

Adds Playwright coverage for startup behavior, native menus, system tray interactions, notifications, and Windows/Linux-only settings flows migrated from Rainforest.

Slice of #3853. E2E coverage validated on #3853. Merge after #3887.

Release Note

NONE

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[saturninoabril]

Thanks Yasser!