Well done for having such a good credit score!
You need to understand that any application for credit, to any company or provider, for any credit card or other form of credit, will “hurt” (more accurately, have a negative impact on) your credit score. It’s unavoidable. So yes, your application for a new card with ANZ or anyone else will put downward pressure on your credit score.
The issue is whether that downward pressure is something that you can live with. One thing that really impacts credit scores is asking “a lot of providers one after the other” (I’m quoting the getcreditscore.com.au website). So if, within the past 6 months, you’ve made no other applications for credit with anyone, then your credit score shouldn’t be affected too badly at all. However, if over the past couple of months you’ve (for example) applied for other credit cards, or taken out a new phone contract, or used a “Buy Now Pay Later” service such as Afterpay, or enquired about or opened a new personal loan, etc, etc … you’ll find that your credit score will probably take more of a hit.
So as far as your credit score is concerned, the issue isn’t merely whether you’ve applied for credit from ANZ. It’s whether you’ve applied for credit with anyone at all.
If you haven’t applied for any credit over the past 6 months, my (educated) guess is that applying for one new ANZ card will barely put a dent in your credit score.
Hope this helps!