When adding a payment method, you may see a small pending charge that will drop off after a couple a days to determine if the payment method is valid. If that small charge cannot be processed, then that payment method is considered not valid.
If you update your billing information or add someone to your Family Sharing group, a temporary authorization hold for a small amount might appear on your statement. Authorization holds are removed by your card issuer or financial institution after a short time.
How apps, content, and subscriptions from Apple are billed - Apple Support
If there was a previous problem with the current payment method you are using or you disputed a charge on the card due to fraud, then you could expect that card to no longer be accepted.
As indicated in this Support Article a valid payment method may be required to download apps, even if they are free, but does not make clear if that can be done by adding money to your Apple Account. It may depend on your region or your transaction history, but I don't know the exact answer to that question.
If you can’t download or update apps on your iPhone or iPad - Apple Support