I suspect the battery/temperature/charge management required of EVs is no small computing feat.
No doubt EVs consume many more chips (maybe as much as an order of magnitude more). The supply chain issues are not necessarily about the chip production volume though, as I'm sure we all know.
Re: battery and charge management, the compute capacity of EVs is certainly greater, but these kinds of capacities are mostly software. Of course there are different valves and controllers (switches) to manage the system and probably a few more sensors in total, but overall these systems are not so complicated from a hardware perspective.
I guess the main source of a need for more chips overall is in the newer higher-end ICE and EV advanced ADAS systems. Those require more sensors, and more sophisticated sensors, and controllers. Designs that are older are less integrated will need more low-end chips for the usual things - power windows, seat adjustments, etc. because there is, in effect, several distinct systems (connected to buttons) that 'compute' the signals to adjust the seat etc.
So the kinds of chips and the variety of chips needed to complete a car varies greatly by model and trim features. The availability of chips is also complicated. Chip manufacturers make much less money for the old types of chips and want to use capacity to make higher-margin chips. Higher end and specialized chips (think radars, etc.) are also competing with other manufacturers making expensive systems (robotics, medical, military, ...)
One supply chain advantage for Tesla is their design is more integrated and directly controlled by a central computer. Also, they just don't bother with a lot of features many might want - like an instrument cluster, HUD, lidar, ...