While I haven't found an official answer (so far), I was able to find a reddit post on their official reddit sub [1] that asks a similar question:
Cashback is based on amount of BNB held in any of my Binance wallets right? Does staked BNBs count into this as well? So if I want to use your crypto visa card with lets say 3% cashback, I can buy appropriate amount of BNB (50) and immediately stake it and it will still count?
Here's the most upvoted reply :
All BNB on Binance counts except DeFi staking. No it does not count immediately, it is an average on 30 days.
So it seems like that you shouldn't have a problem staking BNB as long as it isn't DeFi staking - and as long as you comply with the 30 average days that it takes for you to be edible for the cashback[2]:
* BNB monthly average balance means the average holdings of BNB in your Binance wallets for a period of 29 days before yesterday. The amount of the BNB in the column is the minimum amount for being qualified to the respected cashback level. For example, if your BNB monthly average balance is 5 BNB, which is between 1 BNB for the 2nd level and 10 BNB for the 3rd level, you are assigned to Card level 2 and get 2% cashback on your purchases.
[1]
https://www.reddit.com/r/binance/comments/l9e6ct/binance_card_info_that_is_not_disclosed_in_terms/[2]
https://www.binance.com/en/support/faq/c93fe535bcf4431aa32623ae0a49d4f28
