I recreate your configuration just to test it and if you add show_alert: true message won’t disappear until you press ok.
action:
- service: telegram_bot.answer_callback_query
data_template:
callback_query_id: '{{ trigger.event.data.id }}'
message: >-
Callback received from {{ trigger.event.data.from_first }}.
Message id: {{ trigger.event.data.message.message_id }}.
Data: {{ trigger.event.data.data }}
{{now().strftime("%H:%M:%S %Y-%m-%d")}} Pong, Message from {{ trigger.event.data["user_id"] }}.
show_alert: true