The controller is in the console itself. the memory cards are just a grouping of NAND that interfaces with the onboard controller.
Pretty much this. I don't know why people say the PS5 ssd solution is "so expensive". We basically have 12 512GBit NAND chips and a proprietary on-board controller. Depending on how proprietary the controller actually is, there could be almost zero royalties to be paid. (Sony having basically reeinvented the wheel). Whenever you use a stock ssd controller, there are boatloads of royalties involved.
I wonder though if you can just add another mass grave of NAND-chips to the internal solution and call it a day, or if you need an ssd with a controller. If it's just a bunch of chips, it has to be made by Sony itself (I don't think anyone else is going to do it, no value in it) but would be "dirt cheap" compared to any off-the-shelf solution.