Yes, SPI controllers work very well on ESP8266 and ESP32 boards. e.g. with Bodmer's TFT_eSPI library.
Parallel controllers are more fussy. Too many pins for ESP8266. You need careful wiring for ESP32.
I know nothing about SPFD5408_Adafruit_TFTLCD
I doubt if it would ever work with an 0x9302 controller
What ID is reported by graphictest_kbv on the ESP32 ?
Does it say 0x9302 ?
David.