ios: Nearby-devices picker (AirDrop-style), matching the Mac

Port the nearby picker to iOS: the store polls engine.nearby() while connected
and RoomView shows discovered devices as tap-to-join chips with platform icons,
same as MacTetherApp. pair() joins the device's room.

Dormant on iOS until the multicast entitlement lands (Rust mdns-sd uses a raw
multicast socket iOS blocks without it) — the UI is ready; it'll populate once
the entitlement is granted. No effect when the list is empty.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

ios/TetherApp/Sources/RoomView.swift

@@ -9,6 +9,10 @@ struct RoomView: View {
             VStack(spacing: 0) {
                 connectionBar
                 Divider()
+                if store.connected && !store.nearby.isEmpty {
+                    nearbyStrip
+                    Divider()
+                }
                 feedList
                 Divider()
                 composer
@@ -50,6 +54,46 @@ struct RoomView: View {
         .padding()
     }
 
+    // MARK: - Nearby devices (AirDrop-style picker)
+
+    private var nearbyStrip: some View {
+        ScrollView(.horizontal, showsIndicators: false) {
+            HStack(spacing: 8) {
+                Label("Nearby", systemImage: "dot.radiowaves.left.and.right")
+                    .font(.caption).foregroundStyle(.secondary)
+                ForEach(store.nearby, id: \.id) { peer in
+                    let here = peer.room == store.room
+                    Button {
+                        store.pair(with: peer)
+                    } label: {
+                        HStack(spacing: 6) {
+                            Image(systemName: sourceIcon(peer.source))
+                            VStack(alignment: .leading, spacing: 1) {
+                                Text(peer.name).font(.caption).lineLimit(1)
+                                Text(here ? "in your room" : "tap to join")
+                                    .font(.caption2)
+                                    .foregroundStyle(here ? .green : .secondary)
+                            }
+                        }
+                        .padding(.horizontal, 10).padding(.vertical, 6)
+                        .background(Color.primary.opacity(0.06), in: Capsule())
+                    }
+                    .buttonStyle(.plain)
+                    .disabled(here)
+                }
+            }
+            .padding(.horizontal, 12).padding(.vertical, 6)
+        }
+    }
+
+    private func sourceIcon(_ source: String) -> String {
+        if source.contains("iphone") || source.contains("ios") { return "iphone" }
+        if source.contains("ipad") { return "ipad" }
+        if source.contains("mac") { return "laptopcomputer" }
+        if source.contains("windows") { return "pc" }
+        return "desktopcomputer"
+    }
+
     private var feedList: some View {
         List(store.feed) { msg in
             VStack(alignment: .leading, spacing: 4) {

ios/TetherApp/Sources/TetherStore.swift

@@ -30,12 +30,14 @@ final class TetherStore {
         return a.isEmpty ? RoomIdentity.derive() : roomForAccount(account: a)
     }()
     var feed: [FeedItem] = []
+    var nearby: [Peer] = []   // tether devices on the LAN (empty on iOS w/o multicast entitlement)
     var connected = false
     var lastError: String?
 
     private let deviceID = UIDevice.current.identifierForVendor?.uuidString ?? UUID().uuidString
     private var engine: Engine?
     private var bridge: EngineBridge?
+    private var nearbyTask: Task<Void, Never>?
 
     func connectIfSaved() {
         guard UserDefaults.standard.string(forKey: "serverURL") != nil else { return }
@@ -58,15 +60,33 @@ final class TetherStore {
         engine = e
         bridge = b
         lastError = nil
+
+        // Poll the engine's mDNS-discovered device list for the picker.
+        nearbyTask = Task { [weak self] in
+            while !Task.isCancelled {
+                try? await Task.sleep(for: .seconds(2))
+                guard let self, let engine = self.engine else { continue }
+                self.nearby = engine.nearby().sorted { $0.name < $1.name }
+            }
+        }
     }
 
     func disconnect() {
         engine?.stop()
         engine = nil
         bridge = nil
+        nearbyTask?.cancel()
+        nearbyTask = nil
+        nearby = []
         connected = false
     }
 
+    /// Join a discovered device's room — the "pair" action from the picker.
+    func pair(with peer: Peer) {
+        room = peer.room
+        connect()
+    }
+
     /// Read the system pasteboard (foreground only — iOS bans background reads)
     /// and push it to the room.
     func sendClipboard() {