Having the Zappi in Default FAST mode would appear to rule out some of the potential communication issues when setting the Zappi for timed charging so you would certainly expect it to be straight forward. I presume that, like me, you simply set a maximum percentage and start time with the Tesla. Something that does add confusion to charges starting is the randomised delay on the newer models of Zappi. The car is expecting a charge and, of course, the Zappi nowadays waits anything from a few seconds to 10 minutes before starting to supply charge.
Have you looked at the fault notifications list that the car retains? Also the Zappi retains a list of dated faults and voltage peaks.
The problem I have when trying to track down my own charging issues is that we are in a very rural location with a questionable supply from a rusty transformer up a pole! The voltage fluctuations out here result in the car and/or the Zappi moving the current availability up/down over the period of the charge. However, I can't remember having a charge actually fail in recent times. Though I have seen Tessie app note an occasional interruption for a few minutes with the charge continuing thereafter. (Tessie app has a free trial so could be useful in gathering some data.)
For info my M3 is on software 2023.32.6
I should comment that despite the great reputation that the Zappi has they are most definitely not infallible ... I'm on my third unit since September 2019 ... with 2 free replacements of faulty units having been supplied by MyEnergi. The first one had unexplained crashes and charge failures and my second eventually cooked some internal connections ... I now have the newer version with the built in Hub and Wifi (oh, I also had a failed Myenergi Hub unit prior to this). I give Myenergi full marks for readily and promptly coming up with the free replacements. Combine this with the V5 software problems and we have to remain open to charging issues coming from the charge point side of things even though your history of charging another vehicle suggests otherwise.