Does UITextInteraction have a way to dismiss the edit menu?

Answering my own question....

When you add a UITextInteraction, a UIEditMenuInteraction gets added automatically. So it's possible to iterate through the view's interactions and find the menu interaction using isKindOfClass, and call dismissMenu on that.

It's a bit of a hack, but I've done much worse and it seems to work.

I created an extension to UITextInput that adds methods to let you show/hide the menu. This assumes the custom UITextInput is making use of UITextInteraction.

The following works for iOS 15+ (tested with iOS 15.4, 16.4, 17.4, and 17.5). This has only been tested in development. It arguably uses a private API so I don't know (yet) if this will be approved for App Store apps.

extension UITextInput {
    @available(iOS 16.0, *)
    var editMenuInteraction: UIEditMenuInteraction? {
        return textInputView?.interactions.first { $0 is UIEditMenuInteraction } as? UIEditMenuInteraction
    }

    func showEditMenu() {
        if let textInputView {
            if #available(iOS 16.0, *) {
                // There's no direct API to show the menu. Normally you setup a UIEditMenuInteraction but the
                // UITextInteraction sets up its own. So we need to find that interaction and call its
                // presentEditMenu with a specially crafted UIEditMenuConfiguration.
                if let interaction = self.editMenuInteraction {
                    if let selectedRange = self.selectedTextRange {
                        let rect = self.firstRect(for: selectedRange)
                        if !rect.isNull {
                            let pt = CGPoint(x: rect.midX, y: rect.minY - textInputView.frame.origin.y)
                            // !!!: Possible future failure
                            // This magic string comes from:
                            // -[UITextContextMenuInteraction _querySelectionCommandsForConfiguration:suggestedActions:completionHandler:]
                            // It can be seen by looking at the assembly for the _querySelectionCommandsForConfiguration method.
                            // About 24 lines down is a reference to this string literal.
                            let cfg = UIEditMenuConfiguration(identifier: "UITextContextMenuInteraction.TextSelectionMenu", sourcePoint: pt)
                            interaction.presentEditMenu(with: cfg)
                        }
                    }
                }
            } else {
                if let selectedRange = self.selectedTextRange {
                    let rect = self.firstRect(for: selectedRange)
                    if !rect.isNull {
                        UIMenuController.shared.showMenu(from: textInputView, rect: rect.insetBy(dx: 0, dy: -textInputView.frame.origin.y))
                    }
                }
            }
        }
    }

    func hideEditMenu() {
        if let textInputView {
            if #available(iOS 16.0, *) {
                if let interaction = self.editMenuInteraction {
                    interaction.dismissMenu()
                }
            } else {
                if UIMenuController.shared.isMenuVisible {
                    UIMenuController.shared.hideMenu(from: textInputView)
                }
            }
        }
    }
}