There’s not a whole lot of info posted on this for users, and seemingly no good controls for this feature.
I’d check with your bank app support, and see if they’re using NFC tags with their app. Might also be a card, or a security tag or two-factor token involved.
This might also involve a feature called App Clips. Those can detect NFC tags, including tags on (for instance) payment cards. (I’d suspect this is not App Clips though, given the text of the notification.)
Based on what little is posted, the distance to the NFC tag being detected here is on the order of centimeters to less than a meter; close.