Clarifying Gas Costs After Merge

I've heard here many times that the Merge won't change gas fees because even though there is a higher TPS, its still the same amount of data that Ethereum can store. However, aren't the fees dependent on how POS relates to what a miner would charge? How do we know what the POS fees will be, its hard to imagine its an exact 1:1. Also, I may be completely misrepresenting or misunderstanding the information here, so please correct me if I'm wrong.