The ST7735 displays are very small. You can write to them very fast. Even with a ATmega328.
Bodmer has a faster library than Adafruit_ST7735
There are STM32 versions of the Adafruit_ST7735 library that come with the STM32 Core.
If you want to write your own, the main tricks are:
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Always setAddrWindow() for any shape of rectangle. Even a single line.
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Use hardware SPI. Optimise the SPI for an AVR to avoid gaps between SPI bytes.
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STM32 can write gap-less SPI. An STM32 has got DMA but it is not necessary.
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the Maple Core for STM32 has SPI.write(buf, n) as well as SPI.write_DMA(buf, n)
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regular Arduino Cores have only got SPI.transfer(buf, n) which will overwrite your data.
Good Luck.
Ask if you are stuck with the coding. Note that you can attach files instead of pasting to a CODE window. Or you can ZIP up a complete project and attach the ZIP.
David.