feat(apple): keep iOS transfers alive in the background

iOS suspends the process on backgrounding, freezing the core's network
threads so in-flight transfers stall and never fire notifications. Hold a
UIApplication background-task assertion (BackgroundActivityController) while
transfers/shares are active so iOS grants its grace window — long enough to
finish and notify. Released on foreground, on completion, or on expiration.
No UIBackgroundModes added (keeps App Store validation clean); macOS is a
no-op since it already runs unfocused.

Add a localized iOS-only Settings notice explaining the platform limit so it
doesn't read as a bug.

apple/VniDrop/Core/BackgroundActivityController.swift

@@ -0,0 +1,77 @@
+import Combine
+import Foundation
+#if os(iOS)
+import UIKit
+#endif
+
+/// Keeps the Rust core alive across the app moving to the background, within the
+/// bounds Apple actually allows for a serverless P2P transfer app.
+///
+/// iOS suspends the whole process (freezing the core's network threads) shortly
+/// after the app leaves the foreground. When a transfer or share is active we
+/// take a `UIApplication` background-task assertion so iOS grants its finite
+/// grace window — long enough for an in-flight transfer to finish streaming and
+/// for its completion/failure notification to fire. There is no App-Store-legal
+/// mechanism to keep serving or receiving *indefinitely* while backgrounded, and
+/// `BGTaskScheduler` wake-ups run only opportunistically and cannot detect an
+/// incoming peer connection, so they are deliberately not used here.
+///
+/// macOS does not suspend the process on focus loss, so this is a no-op there and
+/// the core keeps running normally.
+@MainActor
+final class BackgroundActivityController {
+	private let repository: CoreRepository
+
+	init(repository: CoreRepository) {
+		self.repository = repository
+	}
+
+	#if os(iOS)
+	private var assertionId: UIBackgroundTaskIdentifier = .invalid
+	private var idleCancellable: AnyCancellable?
+
+	/// The app moved to the background. Hold the process open while there is live
+	/// work; release as soon as it drains, on return to foreground, or when iOS
+	/// ends the grace window (whichever comes first).
+	func didEnterBackground() {
+		guard assertionId == .invalid, hasActiveWork else { return }
+		assertionId = UIApplication.shared.beginBackgroundTask(withName: "vnidrop.transfer") { [weak self] in
+			// Expiration handler: iOS is reclaiming the window; end cleanly to
+			// avoid the watchdog terminating the app.
+			self?.endAssertion()
+		}
+		// Release the assertion the moment work finishes instead of holding it for
+		// the full window (battery, and it lets the process suspend sooner). Events
+		// still deliver on the main actor while the window is open, so the core's
+		// active counts drop here when a transfer completes.
+		idleCancellable = repository.statePublisher
+			.map { ($0.status?.activeTransfers ?? 0) == 0 && ($0.status?.activeShares ?? 0) == 0 }
+			.removeDuplicates()
+			.sink { [weak self] idle in
+				if idle { self?.endAssertion() }
+			}
+	}
+
+	/// The app returned to the foreground; the process is live again, so drop any
+	/// held assertion.
+	func didBecomeForeground() {
+		endAssertion()
+	}
+
+	private var hasActiveWork: Bool {
+		let status = repository.state.status
+		return (status?.activeTransfers ?? 0) > 0 || (status?.activeShares ?? 0) > 0
+	}
+
+	private func endAssertion() {
+		idleCancellable?.cancel()
+		idleCancellable = nil
+		guard assertionId != .invalid else { return }
+		UIApplication.shared.endBackgroundTask(assertionId)
+		assertionId = .invalid
+	}
+	#else
+	func didEnterBackground() {}
+	func didBecomeForeground() {}
+	#endif
+}