How to programmatically trigger SwiftUI's .refreshable loading animation?

If you are fine with introspecting the underlying UIRefreshControl (i.e. not forward compatible), you can manually refresh the UIRefreshControl using this technique.

@MainActor
class RefreshController: ObservableObject {
    weak var list: UIScrollView?
    
    func refresh() {
        guard let list, let refreshControl = list.refreshControl else { return }
        list.setContentOffset(CGPoint(x: 0, y: list.contentOffset.y - (refreshControl.frame.height)), animated: true)
        refreshControl.beginRefreshing()
        refreshControl.sendActions(for: .valueChanged)
    }
}

@StateObject private var refreshController = RefreshController()
var body: some View {
    List {
        Text("Foo")
        Button("Refresh") {
            refreshController.refresh()
        }
    }
    .refreshable {
        do {
            try await Task.sleep(for: .seconds(1))
            print("Refreshed")
        } catch {
            print("Cancelled")
        }
    }
    // this will only work on the versions you specify here
    .introspect(.list, on: .iOS(.v16, .v17, .v18)) { list in
        refreshController.list = list
    }
}

Otherwise, you will need to recreate your own refresh control. Here is an example:

struct PullToRefresh: ViewModifier {
    @Binding var isRefreshing: Bool
    let onRefresh: () async -> Void
    
    func body(content: Content) -> some View {
        content
            .onScrollGeometryChange(for: CGFloat.self) {
                $0.contentOffset.y + $0.contentInsets.top
            } action: { oldValue, newValue in
                if newValue < -50, !isRefreshing {
                    isRefreshing = true
                }
            }
            // this moves the srollable content out of the way,
            // but it is not animated when pulling down
            // .safeAreaPadding(.top, isRefreshing ? 50 : 0)
            .overlay(alignment: .top) {
                HStack {
                    Spacer()
                    if isRefreshing {
                        ProgressView().controlSize(.extraLarge)
                    }
                    Spacer()
                }
                .task(id: isRefreshing) {
                    guard isRefreshing else { return }
                    await onRefresh()
                    isRefreshing = false
                }
            }
            .animation(.default, value: isRefreshing)
    }
}

This view modifier can be manually triggered setting the isRefreshing binding to true.

@State private var isRefreshing = false
var body: some View {
    List {
        Text("Foo")
        Button("Refresh") {
            isRefreshing = true
        }
    }
    .modifier(PullToRefresh(isRefreshing: $isRefreshing) {
        do {
            try await Task.sleep(for: .seconds(1))
            print("Refreshed")
        } catch {
            print("Cancelled")
        }
    })
}