It should be very straightforward to adapt ILI9341 code.
ST7789 follows the same MIPI compliant user commands.
Manufacturer commands are different. Reading registers is different.
The display appears to be 1.3 inch diagonal. So it is physically smaller than 128x128 ILI9163 displays but higher resolution.
I like SPI displays. If it was 240x320 I would buy one.
David.