Cadence sensors can give issues, move out of position or the cable can have poor connections etc. That is probably the first thing to look at as its one of the mechanical aspects of the bike. There are also fuses I'm sure in the battery and components in the controller that can fail like the mosfets. Normally the wheel will do something if its given power so its more likely to be a fault prior to that.
I think the Crosscity is a fully open non-proprietary ebike system however the battery fitting inside the downtube of the frame makes it difficult to replace at a reasonable price but presumably if you didn't mind a battery on a rear rack or somewhere else you could fit a cheaper battery. It's 313Wh. You could probably pick up a plastic wrapped battery to the same spec for less than £90 delivered on aliexpress but the official replacement battery probably costs over £200 maybe £300 or more.
A quick look shows a 36V battery pack capable of 20A output, not quite the same overall capacity but small enough to fit into a saddle bag and provides 245Wh at about £60 delivered. The 36V 6800mAh battery.
https://www.aliexpress.com/item/4001009534335.html
How long do batteries last without any charge at all. Normally they protect themselves so won't discharge beyond 20% capacity and that 20% capacity will take many months to fully discharge and end up destroying the cells I would estimate 9 months to perhaps 18 months but always worth trying to recharge the pack at any point. Bosch batteries self-brick, as the battery becomes discharged as soon as the BMS has too low a voltage the BMS will stop working permanently as a protection method for their highly proprietary batteries, this prevents you changing the cells yourself or re-using the BMS so those batteries can self-brick very easily perhaps in 6 months or more of not being charged. Of course Bosch batteries are extremely expensive for their capacity. The only good thing is the BMS dies long before the cells so if you catch it at the right time you can strip the battery pack of the cells to use in another non-proprietary ebike battery pack and the Bosch battery packs always use good cells.
Also batteries with bluetooth circuits. The bluetooth circuit is permanently enabled so this creates a additional drain that can kill the battery in a shorter period of time perhaps 3 to 6 months. It needs a tiny amount of current but on for 24/7 it will kill a battery.