How can you prompt text in an alert?

Here is how you create an alert with a TextField.

Declare in the VC

     var alert : UIAlertController?

I have embedded in an IBAction to call the alert from a UIButton.

    @IBAction func testAlert(_ sender: Any) {
   
        //1. Create the alert controller.
        alert = UIAlertController(title: "Search City", message: "City name ", preferredStyle: .alert)
      
        //2. Add the text field.
        alert?.addTextField(configurationHandler: { (textField) -> Void in
            textField.placeholder = ""
            textField.keyboardType = UIKeyboardType.emailAddress // For instance
          // alertTextFieldDidChange activate OK button
            textField.addTarget(self, action: #selector(self.alertTextFieldDidChange(_:)), for: UIControl.Event.editingChanged)
        })
        
        //3. Grab the value from the text field.
        let yesAction = UIAlertAction(title: "Search", style: .default, handler: { (action) -> Void in
            let textField = self.alert?.textFields![0] 
            if textField?.text! == "" {
                print("empty")   // Just for testing, should be removed
            } else {
                print("not empty", textField?.text! ?? "")      // Just for testing, should be removed
            }
        })
        yesAction.isEnabled = false.
        alert?.addAction(yesAction)     // This will be actions[0]
      
        // 4. Present the alert.
        self.present(alert!, animated: true, completion: nil)
      
    }

The handler where we activate OK as soon as a textField not empty

    @objc func alertTextFieldDidChange(_ sender: UITextField) {

     alert?.actions[0].isEnabled = sender.text!.count > 0
    }

For information, from doc:

UIAlertController

var actions: [UIAlertAction]

The actions that the user can take in response to the alert or action sheet.

var actions: [UIAlertAction] { get }

Regular AppleScript is limited to what you can do with display dialog, but AppleScriptObjC can be used to access the Cocoa APIs. For something like the password input, you would be looking at using an NSAlert with a couple of NSTextFIelds in an accessory view.