If the original flight was a fully flexible fair you would have had the option of a refund to the original payment method i.e credit card. If it was a sale or discount fare the default method prior to October 2020 was a flight credit (good for 12 months). If the credit didnt suit you needed to request a refund to origial payment form at the time Qantas cancelled the original flight (back in 2020) and before the original departure date, not now 2 years later.
When Qantas converted unused flight credits to a TPs last Oct/Nov, they actually extended the expiry to 31/12/22 in recognition there was limited chance to travel in 2020 and 2021.
You do not need to call Qantas to book a flight using the TP, you can do it online; and it can be used for QF operated or partner operated flights provided you ook through QF.
Im not sure why you think QF doesnt fly internationally, they have resumed flights to UK (although JFK flights are pending), USA, Fiji, NZ, Thailand, South Africa, Singapore and India. Its true flights to Chile and Bali havent resumed. QF is certainluy flying to more international destinations than the other Australian airline Virgin.
QF will be resuming more international routes in the coming months, so plenty of time to still use your TP.
Irrespective of the airline if you want to be guranteed a full refund you need to book fully flexible fares.