Looks like Costco have finally launched a digital membership card via their app for iOS and Android.
https://www.costco.com.au/digital-membership
FAQs from the website:
Q: How do I get my Digital Membership?
A: Instructions on how to access your digital membership can found found [sic] at www.costco.com.au/digital-membership/guide/interactive
Q: Where can I use my Digital Membership?
A: You can use your digital membership to enter the warehouse and at the Checkout and Self-Check out Kiosks (Self-Check Out not available in all warehouses)
Q: Will my digital membership work at the Fuel Station?
A: Not at the moment, but we are working on a solution to bring this feature to our members in the near future.
Q: Can I add my Digital Membership to the Wallet on my device?
A: At this stage, your digital membership can only accessed through the Mobile App.
I just downloaded the app on Android and logged in to try and set it up.
Firstly, "The Digital Membership Card" button was not visible on the "My Costco" tab for me so I thought maybe they had launched the PR campaign but not actually rolled out the app updates yet however a little bit of playing around on the app and I inadvertently got it to show by doing a swipe down and hold motion as if I was refreshing the page (similar to how the KFC app used to be for accessing the Secret Menu). In doing this the button appears for about 1 second and I was able to quickly press it and start the process of setting up my digital card. I've taken my photo but still need to go into the warehouse and have it verified as per the requirements.
Not sure if the inability to plainly see the button is because of my phone screen/size (Galaxy A52) or just a poorly implemented porting from iOS to Android or because I'm a Business member or something else entirely.
For people who fill up at Costco you still need the physical card for fuel but I guess now you can just leave the card in the car and you have the app on your phone for everything else. Saves you carrying it around everywhere if you only use one vehicle regularly.
Thanks OP. Updating App noow