Don't Singapore Airlines need to provide a passport number to book a ticket in official website?

That's right. Just make a trial order in official website. Singapore Airlines official website /home does not need to fill in the passport number. Some airlines need to fill in their passport numbers when booking tickets in official website, while others don't, such as Singapore Airlines. However, in order to be unified and convenient, passport information is required for booking through agents.

There is a disclaimer on Singapore Airlines official website about passport information: every passenger must hold a valid passport (and visa if necessary) before entering the country through each destination in the flight itinerary. Singapore Airlines will not be responsible if passengers are refused entry and/or repatriation by any local authorities.