For anyone interested, my application went like this:
14/1: Applied
16/1: They emailed me asking for payslips. I think I uploaded five of my most recent ones.
17/1: ANZ called me and asked me for two additional payslips, as my income for one period was lower than others (I was in Singapore for a bit over a week and I'm casual). I sent them four more payslips, just to be safe. They also asked for bank statements for the past six months.
24/1: They called again and asked for a payslip for a specific fortnight, even though I had already supplied it. They also asked for bank statements up to the current day, rather than the ones I provided ending 31 December.
26/1: Called again and said that I needed to visit a branch and verify my ID, as the credit card application had created a duplicate profile and those two profiles needed to be merged to proceed to the final step. This was because I had an ANZ account, opened ages ago, that was never verified or something to that affect.
27/1: Visited the branch and completed the merge of the accounts and then called ANZ later on and they said it was all completed and ready for the outcome. I then received the approval email.
2/2: Offer letter arrived.
6/2: Card arrived and activated.