There are vampire 12 V loads that will discharge the 12 V battery a bit over a week just as with all modern vehicles (e.g., keyless entry system, telematics module, system clock, burglar alarm system if armed). As EvanstonI3 wrote, your 12 V battery will be fine unless it's very weak and about to die anyway.
In general, the high-voltage (HV) battery pack is disconnected from all HV loads when an i3 is turned off. Exceptions are when the doors, hatch, or frunk are locked/unlocked or opened/closed, when charging is active, when cabin or battery pack preconditioning is active, or for an hour to charge the 12 V battery when its voltage decreases beyond a certain limit. After any of these events, the HV system could remain on for as long as 30 minutes discharging the HV battery pack slightly. The self-discharge rate for Li ion battery cells is very low (~1% per month in my experience), so the charge level of your battery pack wouldn't decrease noticeably over a week.
To minimize the battery cell degradation rate on its newer EV's, BMW recommends not fully charging routinely unless maximum range might be needed. BMW might have learned from replacing many 2014-2016 i3 battery packs under warranty due to excessive cell degradation. Fortunately, later i3 battery packs seem to be much more resistance to excessive cell degradation. Unfortunately, the i3 doesn't allow its charge level to be limited when charging, so leaving an EVSE plugged in would fully charge the battery pack with it remaining at a full charge for a week. This isn't the best practice, but it almost certainly wouldn't result in enough cell degradation to be noticeable. Another concern is that a power surge could cause expensive damage to the on-board charger, so I never leave my EVSE plugged in after I finish charging.