My first choice for M2 D4L heater would be an Eberspacher Easystart PRO - SEE WEBLINK - has great diagnostics plus timer and temp regulation functionality with built in temp sensor option included
https://www.butlertechnik.com/item/Eberspacher/EasyStart-PRO-for-Airtronic-S2-M2-and-Hydronic-S3-12v-24v-Heaters-221000352200/619
Your 801 controller unfotunately is NOT compatible with M2 D4L Eberspacher heater. You are correct in thinking that an 802 controller would work, but to be honest an 802 controller would definitely not be my first choice, it's functionality is very limited on the M2 D4L ( it does not have, error fault code reading function, so no diagnostics for future-proof operation.
My second choice Easystart Select - see weblink - simple operation, diagnostics but less comprehensive, no internal temp sensor
https://www.butlertechnik.com/item/Eberspacher/Easy-start-Select-controller-Airtronic-or-Hydronic-heater-221000341300/6SE
Thanks for getting in touch, any questions just email sales@butlertechnik.com
David