For anyone interested, there is now support for the BTT TFT35-E3 V3.0 Display Touch Screen (https://www.biqu.equipment/products/btt-tft35-e3-v3-0-display-touch-screen-two-working-modes).
This work was done as part of an internal project to use this 3D printer controller as a custom controller. Based on our own experience, and given their specs, hardware, and relatively low-cost, they are excellent for Arduino projects needing a touch screen interface. A separate touch screen/Arduino board would cost twice as much. We only added support for this one version of the board though, but it should be straight forward to add support for the other versions as well.
You can checkout the code over at github: GitHub - ns96/BTuino: BTuino is a port of the BigTreeTech TFT35-E3 V3.0 Touch Screen Display for the Arduino IDE