It is certainly possible to have datalogging on a BMS if it is run by an MCU, or some of the dedicated BMS chips. Many of the laptop battery BMS chips i investigated 2-3 years ago can do this, either to internal memory or to an external serial EEPROM. Most are not USB-readable, but instead use a dedicated 2-wire interface or similar, thru the regular battery port, to tell the laptop what the battery condition is.
It's much less likely that a typical ebike will have anything like that, as they seem to be made for lowest cost rather than for protecting the company's warranty-coverage interest, leaving it to a human to determine whatever has gone wrong and under what conditions. Usually the BMS is just made to keep teh battery from ever being used outside of the conditions the warranty would cover, so if indeed the conditions were exceeded it would just shutdown until power is cycled. If it allows the conditions to be exceeded then usually either it's badly designed or faulty, and the warranty should cover it's replacement anyway (in my opinion, not necessarily the company's

).
If it did have logging circuits, they may not be accessible outside the case, as there is no reason for htem to be; they're only for factory use so only the factory has to have access. No reason to spend more money on an external connector, waterproofing, etc., for a connector the user cannot even use (since it is likely it would require special equipment and software to communicate with it anyway).
Most ebike BMSs do not have anything to interrogate, though.
FWIW, if the idea of connecting up the celllog or other cell-level monitor up and determining state of charge on there is daunting, I expect that reverse-engineering the BMS to find out if it has any datalogging, and then figuring out it's protocols, etc., finding or creating software to read them and their data, and so on, is all likely to be far beyond your desire to try.
But I also expect that in order to do either of those things, you'd have to open the battery pack up to get to the BMS connections inside, and if that voids the warranty, you would not want to do so either way.
