Why do you use the line for the 4.2" b/w if you have a 2.9" 3-color display?
//GxEPD2_3C<GxEPD2_290c, GxEPD2_290c::HEIGHT> display(GxEPD2_290c(/*CS=5*/ SS, /*DC=*/ 17, /*RST=*/ 16, /*BUSY=*/ 4));
This should work for ESP32.
And of course display.init() only will not produce any output. Consider using GxEPD2_Example.ino