Good Mornig Jean-Marc,
thank you for responding so quickly. I understand the problem with the ESP memory is to small for the graphics buffer. Is this also a problem with the ESP32 or does it have enough memory for that? I do not have an ESP32 yet but if it will work (better) I´ll going to buy some.
I agree with Jean-Marc, the new HAT ist weak with 3.3V. I use a (old version 640x384) 7,5" 3-colour Display with an ESP-07 for showing a bmp file that is downloaded all 15min. As deep sleep of the ESP where not very stable I did a workaround with an Texas-Instruments Timer TPL5110. It just switch on a Mosfet that ist feeding the LDO for the ESP and the Dislay. After donwloading the bmp the ESP sends a done signal to the timer and it cuts off everything again. Quietcent current of the timer arround 30nA!
https://www.waveshare.com/product/7.5inch-e-paper-b.htm (Link is to the newer one)
https://www.bastelgarage.ch/esp-07-esp8266-wifi-serial-modul-micro-controller
https://www.ti.com/lit/ds/symlink/tpl5110.pdf
I had some problems with busy time out as well. For me I changed the wiring and using different Pins. But be aware of the HW SPI Pins. Don´t use them for other signals here.
I recommend you to override the HAT LDO and Levelshifter as you don´t need them with the ESP.