The title seems to imply that the technology for boring the tunnel is Tesla derived, while it is related to the whatever vehicles that will be used in the tunnel once it will have been bored "traditionally".
EDIT: actually, from looking at , Tesla says it was based on licensed Lotus tech, but most definitely not an electrified Elise. TIL.
 - https://www.tesla.com/blog/lotus-position
And they need an amount of power that very doubtfully can be delivered by batteries.
It is a bit of time that I don't deal with those smallish diameter TBM's, of 14 feet or so but to give you a comparison, a 22 feet one has usually a head (just the head) driven by some 6 x 300 or 350 kW electric motors.
In the FAQ of the boring company:
they mention diesel locomotives, but personally I have only seen electric (battery) locomotives used during TBM excavations.
And the plan is to make their TBM's speedier by augmenting the power (to the head), besides optimizing cycles and what not, thus most probably the TBM itself will be powered "traditionally" by cable electricity.
The Boring Company FAQ only says 3x. They also want to do cutting and ring installation simultaneously, rather than alternately. TBMs have already been built which do that.
Here's the fastest TBM in current use. Best month, 702 meters. Worst month, zero, when they hit a cavern and had to stop to fill it with gravel and grout before proceeding. Tunneling has surprises like that. That machine has both a hard-rock and a pressure-balance mode. Switching is a big deal, with lots of cutter changing.
One place Tesla might make progress is at the back end of the TBM. There's a huge amount of activity in back. Behind the TBM, there's usually a narrow gauge railroad track, and two tracks if there's room. Dirt cars are brought forward, filled with dirt, and sent back out. Ring segment cars bring ring segments forward. Work cars bring workers, tools, and spare parts. Track cars bring more track sections, to be laid behind the TBM. The TBM has machinery for laying track, loading and unloading cars, and moving cars from one track to the other.
What if all those work cars were self-driving battery-powered vehicles? Get rid of all the tracks, use self-driving vehicles with 4-wheel steering, and have them position themselves exactly where they're needed. Dirt cars stop under the output conveyor, fill, and leave. Segment cars maneuver into position
to where the segment assembly arm (a big robot arm) can remove the segments. No more track section cars.
You'd need vehicles which run well on the bottom of a round tube without being centered, so they can pass each other. That could eliminate about half the gear at the back end of the TBM.
The smaller the tunnel is, the smaller is the size of the ventilation tubes that can be used, and thus you need more power to push the air inside.
The amount of air needed by an electric motor is "0", whilst the amount of air needed by a combustion engine is something that needs to be evaluated on a case by case basis, normally the rule of the thumb is 4 cubic meters per minute for each Diesel HP (i.e. with kW's 5.4/KW).
And you have to assure anywyay some air to the people, usually 3 cubic meters per person per minute is used.
And there is anywyay a limit to the pressure with which you can pump air in, because the "return speed" is usually limited to a maximum of 0.5 m/s (as higher speed may cause the transportation of dust and particles).
And then of course the longer the tunnel is the more powerful must the ventilating fans be, we are talking of several hundreds of kW to power these fans.
The method generally used is "positive pressure".
I.e. there is a single pipe or duct through which the air is pushed till the excavation front.
The air, having no possible way out is forced to go back towards the tunnel opening.
Since usually the most activities are near the excavation front there is concentrated the clean air, while the one returning back is "contaminated" by the CO2 and other fumes at the excavation front.
The 3 m3/min per person and 4 m3/min per HP are common rules of the thumb to calculate the amount of air, and is in practice a "large" allowance since it is calculated with the maximum possible number of people and with the theoretical power of diesel engines (that never run at 100% throttle), and it has to take into account the said effect of contamination so that people working in the tunnel (not a the the excavation front) still get enough clean air.
Moreover it is not a "continuous fine regulation", fans have normally a finite number of speeds, so you are always using the speed (and the number of fans) calculated for the "longest stretch". As an example for the first 200 mt of excavation you have one fan at 1st speed, the next step, switching to 2nd speed is good up to (say) 400 meters, and you switch to 2nd as soon as you get past 200 mt, and so on.
Which makes it interesting that the 4 cubic meters per HP is about 10 times the allowance for contamination as the 3 cubic meters per person. Everyone shares the higher contamination level whenever the engines are active.
In such a ventilation scheme during the works most personnel is near or in the immediate vicinity of the excavation front, they have "non-contaminated" "fresh air" at all times.
You get some "contaminated" air only during the time it takes from the tunnel entrance to the excavation front, and in some circumstances people making maintenance or other works far from the excavation front.
As said the quantity of fresh air fanned in is much more than what actually "needed", there are sensors for the contamination and all in all the air you breath in any modern tunnel during construction is much, much better than what anyone breaths everyday in a trafficked city.