Gift card or code balance limit error happens to me when I try to add a gift card

Try it again tomorrow. I believe it calculates your starting balance daily.

Since your starting balance today was $1600, it would only let you add $400. Tomorrow your starting balance will be $600, so you will be able to add $1400 if you wish.

December 2020 post Apple account balance excess limit - Apple Community showing notice saying:

"Exceeds Balance Limit.

Your gift card or code could not be redeemed at this time. Your daily starting balance and contributions cannot exceed $2,000.00"

and a similar one from Nov. 2020 When i recharge with gift card, it said “… - Apple Community

Sept. 2020 post iTunes $2000 balance limit? - Apple Community also mentions a $2,000 limit.

August 2020 post Why my apple account balance cannot excee… - Apple Community showing a notice saying:

"Exceeds balance Limit.

Your Apple Account balance cannot exceed $2,000.00. Your gift card or code could not be redeemed at this time.

June 2021 post Apple gift cards - Apple Community

Read the message carefully. It has several conditions and make sure you are not exceeding any of them. You have $600 now, but did you deposit a large amount earlier which might means you are trying to add more than $2,000 today??

It has been reported here many times that there is a limit of $2000 in your Apple Account balance. Is that the case for your account balance?

Thank you for the update!

I have heard that too, but do not know if it is true or if they use an average daily balance over a week, but I would recommend trying it again tomorrow.

Post back your outcome and it will help other users facing the same problem and you may be able to finally answer that question.