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Yes, you can connect it to your Mega2560 if you want. Just buy 21 level shifters for the TFT. And a few more for the SD if you want to use that.
It is a lot of hard work wiring up all those level shifters.
You could buy a 40-pin Adapter shield which will be easier. Just lots of plain wires from your display to the appropriate pins on the 20x2 socket.
It is much simpler to just buy a STM32 board with a matching socket. No need for level shifters.
David.