iOS Share Extension: pick the destination inside the share sheet

SwiftUI folder picker in the extension (WebDAV PROPFIND), account shared via
a Keychain group, upload on a background session that outlives the extension
and is finished by the app. The inbox + notification hand-off remains as the
fallback (no account / 'choose later'). Shared code moves to ios/Shared.

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>

ios/Shared/ShareUpload.swift

@@ -0,0 +1,73 @@
+import Foundation
+
+/// Starts the Share Extension's uploads on a background `URLSession` that
+/// outlives the extension. The extension process is torn down as soon as its
+/// sheet closes; because the session has a `sharedContainerIdentifier` and
+/// the same identifier is recreated by the app at launch
+/// (`TransferManager.reconnect`), the *app* is what gets relaunched to
+/// receive the results, post the summary notification and clean up.
+/// Compiled into both targets.
+enum ShareUpload {
+  static let sessionIdentifier = "dev.ayushya.noo.transfers.share"
+
+  static func configuration() -> URLSessionConfiguration {
+    let config = URLSessionConfiguration.background(withIdentifier: sessionIdentifier)
+    config.sharedContainerIdentifier = AppGroup.identifier
+    config.sessionSendsLaunchEvents = true
+    config.isDiscretionary = false
+    config.waitsForConnectivity = true
+    return config
+  }
+
+  /// A `PUT` for [item] into [remoteFolder] - shared by the extension's
+  /// [enqueue] and the app's own uploads so both build requests identically.
+  static func uploadRequest(for item: SharedItem, account: SharedAccount, remoteFolder: String) -> URLRequest? {
+    guard
+      let url = WebDAV.fileURL(
+        serverUrl: account.serverUrl,
+        username: account.username,
+        remotePath: WebDAV.join(remoteFolder, item.name)
+      )
+    else { return nil }
+    var request = URLRequest(url: url)
+    request.httpMethod = "PUT"
+    request.setValue(account.authHeader, forHTTPHeaderField: "Authorization")
+    if let modified = (try? FileManager.default.attributesOfItem(atPath: item.path))?[.modificationDate] as? Date {
+      request.setValue(String(Int(modified.timeIntervalSince1970)), forHTTPHeaderField: "X-OC-Mtime")
+    }
+    return request
+  }
+
+  /// Queues every item (already copied into the App Group by the extension)
+  /// and returns once the system has accepted them.
+  static func enqueue(items: [SharedItem], account: SharedAccount, remoteFolder: String) throws {
+    guard !items.isEmpty else { return }
+    let batch = UUID().uuidString
+    // No delegate here: the extension is gone before the results arrive.
+    let session = URLSession(configuration: configuration())
+
+    var tasks: [URLSessionUploadTask] = []
+    for item in items {
+      guard let request = uploadRequest(for: item, account: account, remoteFolder: remoteFolder) else {
+        throw TransferError(message: "Invalid server address.")
+      }
+      let task = session.uploadTask(with: request, fromFile: URL(fileURLWithPath: item.path))
+      task.taskDescription =
+        (try? JSONEncoder().encode(
+          TransferTaskInfo(
+            kind: .upload, batch: batch, name: item.name, remoteFolder: remoteFolder, stagedPath: item.path)
+        )).flatMap { String(data: $0, encoding: .utf8) }
+      tasks.append(task)
+    }
+    TransferBatchStore.save(
+      TransferBatch(kind: .upload, remoteFolder: remoteFolder, total: tasks.count, succeeded: 0, failed: 0),
+      id: batch)
+    tasks.forEach { $0.resume() }
+    session.finishTasksAndInvalidate()
+  }
+}
+
+struct TransferError: LocalizedError {
+  let message: String
+  var errorDescription: String? { message }
+}