What is the ruling on using a credit card that is charged from the user's balance and used for online purchases and hotel bookings, when it is issued by the same company that issues interest-based (riba-based) cards (Mastercard)?

It is permissible to use a Visa card if it is free from শরী'আ-prohibited elements. If you pay money first, which is called "charging the card," and then purchase goods with the card, there is no harm in that. It does not matter if the company issuing this card also issues interest-bearing cards.