Show connection progress at app startup instead of flashing screens

mac/Sources/Byre/Tailnet.swift

@@ -130,14 +130,15 @@ final class Tailnet {
     private(set) var state = "Starting"
     private(set) var authURL: URL?
     private(set) var service: TailnetInfo?
+    private(set) var searched = false
     @ObservationIgnored private var servers: [URL] = []
 
     var running: Bool {
         state == "Running"
     }
 
-    var signedIn: Bool {
-        running && service?.state != "NeedsLogin"
+    var needsLogin: Bool {
+        state == "NeedsLogin" || state == "NeedsMachineAuth" || service?.state == "NeedsLogin"
     }
 
     private init() {
@@ -181,19 +182,52 @@ final class Tailnet {
 
     private func discover() async {
         while true {
-            if running {
-                for origin in servers where !Servers.shared.origins.contains(origin.absoluteString) {
-                    let api = API(origin: origin)
-                    if (try? await api.client.getStatus().ok) != nil {
-                        log.notice("found \(origin.absoluteString, privacy: .public) on the tailnet")
-                        Servers.shared.add(origin)
-                    }
-                    api.session.finishTasksAndInvalidate()
-                }
+            guard running else {
+                try? await Task.sleep(for: .milliseconds(500))
+                continue
             }
+            let candidates = servers.filter { !Servers.shared.origins.contains($0.absoluteString) }
+            let found = await withTaskGroup(of: URL?.self) { group in
+                for origin in candidates {
+                    group.addTask {
+                        await Self.probe(origin) ? origin : nil
+                    }
+                }
+                var found: [URL] = []
+                for await origin in group {
+                    if let origin {
+                        found.append(origin)
+                    }
+                }
+                return found
+            }
+            for origin in found {
+                log.notice("found \(origin.absoluteString, privacy: .public) on the tailnet")
+                Servers.shared.add(origin)
+            }
+            searched = true
             try? await Task.sleep(for: .seconds(10))
         }
     }
+
+    private nonisolated static func probe(_ origin: URL) async -> Bool {
+        let api = API(origin: origin)
+        defer {
+            api.session.invalidateAndCancel()
+        }
+        return await withTaskGroup(of: Bool.self) { group in
+            group.addTask {
+                (try? await api.client.getStatus().ok) != nil
+            }
+            group.addTask {
+                try? await Task.sleep(for: .seconds(5))
+                return false
+            }
+            let ok = await group.next() ?? false
+            group.cancelAll()
+            return ok
+        }
+    }
 }
 
 struct TailnetLoginView: View {