Hello @songgyosu and welcome to the community!
So you have worked with a STM32F746-dk board that uses a MT25Q128 and everything worked fine and now you want to use a MT25Q256 right?
I do not understand how you implemented that memory, did you create a completely new board with new PCB to which you soldered a STM32F746 MCU and a MT25Q256? Did you unsoldered the MT25Q128 that was on the STM32F746-DK board and replaced it with the MT25Q256(because you say "when replacing the MT25Q256 on the stm32F746-disc board")?
Even if the 2 memories are very similar and seems to only have their size that is different, their implementations is actually different.
Here is an example of differences in the 2 datasheet, we can see that there are differences in timings for dual and quad mode:

There might be even more differences that should be implemented.
However, I don't think there should be any modification done on TouchGFX, only on STM32CubeMX and in code.
Regards,