Those screenshots look like it should work. Please temporarily set the Dialogue Manager's Other Settings > Debug Level to Info and reproduce the issue. This will log activity to the Console window, which should help you identify the problem.
Thanks for posting the logs. They show that the underlying conversation engine is properly the correct dialogue entries. But it's not appearing in the UI.
Are there any warnings in the Console window? Make sure the Console isn't filtering out warnings.
If there are no warnings, please reproduce the issue and inspect the dialogue UI's subtitle text GameObject. Does the Text / TextMeshProUGUI component contain the text "Son, are you wake up?" (Side note: Consider changing it to "Son, are you awake?")
If the Text / TextMeshProUGUI component does contain the text, check if the GameObject is active.
If it doesn't contain the text, are you pausing the game during conversations? If so, what is the Dialogue Manager GameObject's Other Settings > Dialogue Time set to?