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/WebDAV.swift

@@ -0,0 +1,53 @@
+import Foundation
+
+/// URL building for a Nextcloud account's WebDAV files root. Pure functions
+/// (no networking), so they're unit-tested in `RunnerTests`.
+enum WebDAV {
+  /// `urlPathAllowed` minus "/", so a file name containing a slash-like
+  /// character can't introduce an extra path segment.
+  private static let segmentAllowed: CharacterSet = {
+    var set = CharacterSet.urlPathAllowed
+    set.remove(charactersIn: "/")
+    return set
+  }()
+
+  static func encodeSegment(_ segment: String) -> String {
+    segment.addingPercentEncoding(withAllowedCharacters: segmentAllowed) ?? segment
+  }
+
+  /// `<server>/remote.php/dav/files/<user>/<remotePath>` - [remotePath] is
+  /// relative to the user's root, with or without a leading slash. A server
+  /// installed under a sub-path (`https://host/nextcloud`) keeps it.
+  static func fileURL(serverUrl: String, username: String, remotePath: String) -> URL? {
+    var base = serverUrl
+    while base.hasSuffix("/") { base.removeLast() }
+    let segments = remotePath.split(separator: "/").map { encodeSegment(String($0)) }
+    var url = base + "/remote.php/dav/files/" + encodeSegment(username)
+    if !segments.isEmpty { url += "/" + segments.joined(separator: "/") }
+    return URL(string: url)
+  }
+
+  /// `folder` + `name` with exactly one slash between them.
+  static func join(_ folder: String, _ name: String) -> String {
+    folder.hasSuffix("/") ? folder + name : folder + "/" + name
+  }
+}
+
+enum LocalFiles {
+  /// A URL in [directory] for [name] that doesn't exist yet: "a.txt", then
+  /// "a (1).txt", "a (2).txt"... - so a second download of the same file
+  /// never overwrites the first.
+  static func uniqueURL(in directory: URL, name: String, fileManager: FileManager = .default) -> URL {
+    let candidate = directory.appendingPathComponent(name)
+    if !fileManager.fileExists(atPath: candidate.path) { return candidate }
+    let ext = (name as NSString).pathExtension
+    let stem = (name as NSString).deletingPathExtension
+    var index = 1
+    while true {
+      let numbered = ext.isEmpty ? "\(stem) (\(index))" : "\(stem) (\(index)).\(ext)"
+      let url = directory.appendingPathComponent(numbered)
+      if !fileManager.fileExists(atPath: url.path) { return url }
+      index += 1
+    }
+  }
+}