The screen is supported by Arduino_GFX. ST7701S is supported in that library. Not sure if ESPhome can use it though.
openHASP doesn’t make much sense on this device since there is no real touchscreen…
So the limiting factor is no touchcontroller, the display should work.
Taking a look at that video (and I saw your comment on it) it would certainly imho be good with openhasp, if you watch it, scrolling through menus and pressing the one button to select. It’s not really that different to a touch experience. All imho of course, and coding is not my superpower.