Have you tried to run it on PHP 8+? Also, module is updated to run in PS 8.1?
Last official version is 3.4.6 / Last update 01/2018 up to PS version 1.7.6
Are you using default presta checkout or custom one?
I've had similar issue with other payments module on custom checkout. What i did i have removed both payments and checkout module. Then i install payments and then checkout. It's working fine now. Seems in some cases checkout dont see new payment options, when you added after.
Also ask developer if they have any updated versions official one or thise one https://www.modulebazaar.com/prestashop-eway-payments-australia-module/00100024