I don't know the model you have, but in general, for Li-ion batteries the under-voltage protection (when the BMS disconnects the battery) is somewhere at about 2.8V or so, but the circuit powered by the Li-ion cell should never discharge the battery that low on purpose. 2.8V is a protection for malfunction and extreme situations only.
During normal use the battery should never go that low. There is not much energy left under 3.2 ... 3.5V, so there is no point by over discharging the battery. Same with the over voltage protection, the BMS will disconnect the cell at about 4.3V or so, but you should never go over the specified 4.2V top charging voltage.
These limits might depend with the exact type of battery. For example, there are Li-ion of 3.6V nominal, or 3.7V (most common these days), or 3.8V or even 3.85V nominal (for example Samsung phones, some Xiaomi too), which are charged up to 4.4V instead of only 4.1V (for 3.6V nominal type) or 4.2V (for the 3.7V nominal type).
Other Li based rechargeable are much lower nominal voltage than that (IIRC 3.2V or so), but they are not that common. The vape and/or cigarette heaters I've opened they were all heaving 3.7V nominal and 4.2V top charging type of Li-ion.
About the battery level indicator, that might not be a coulomb meter. Maybe they just count the number of puffs and consider an average energy taken with each puff, but I never looked into that, only speculating.
You can still reuse the vape battery without knowing its exact discharge state. Just charge it more often, or make the load circuit to detect when the voltage goes lower than 3.5V or so.