Even before doing any research, I can tell you that all other power expenditures are pretty negligible compared to the the amount of energy required to produce the light that feeds the plants... but here are all the numbers anyway:
Water distribution is pretty cheap in terms of power because of how hydraulic systems work. If you have water to store in an elevated place, then every pipe attached to it will have water pressure no matter how far laterally it travels. If you build a dam that raises a reservoir above the level of your farms, then that means your water is absolutely free (in terms of energy to distribute.) Even if you need to pump the water https://www.engineeringtoolbox.com/pumping-water-horsepower-d_753.html show that a 1kw pump can life over 100 liters 15 meters per second. Wheat needs 100-125mm of rainfall a year. That is about 455 liters per year per acre; so, unless your farm is at the top of a highrise building, whole system could generally have it's entire annual water pumping needs meet off of the power stored by a AA battery.
Robotics (aka Fertilization/soil control/all the equipment)
Farming indoors requires a lot less of things like weeding, pest control, etc. While this is hard to find exact specs on, I'd imagine you probably are not using much more power than a laptop consumes simply because there is not really that much to do 99% of the time but have systems on standby waiting to scan something or controlling a few nozzle servos to start/stop watering. This is just a ballpark guess, but I would be surprised if you actually needed more than 4-5 kWh/day.
Air conditioning and filtration will vary a lot relative to your setup. In general, wheat prefers 70-80°F (21-27°C). If you are building in an archaeology located in a desert, this could take a lot more A/C to keep cool, but if you are in a cooler region where you design your vertical farm buildings to have a natural heat-sink shape, your AC could be practically passive. If you assume a home needs a 20 BTU/sqft AC running an average of 3 hours a day to maintain these temperatures during growing seasons where wheat is normally grown to offset the heat of the sun, then an acre of enclosed farmland should be fine with an 871,200 BTU HVAC system. That will make your HVAC system require about 261.36 kWh/day.
Cannabis and wheat have similar light requirements; so, your indoor farm will probably need about 40-50 watts worth of LED lighting per square foot to grow. That means your wheat will need a total of 1960.2 kW worth of lighting which will need to be on for an average of 14hrs a day to simulate grow season daylight time. That is a total of 31,363.2kWh/day.
My personal experience with my battery powered weed wacker is that a 2Ah 20v battery can take out about 100sqft of tall thick grass which would be comparable to the process of harvesting wheat. 2Ah @ 20v = 40Wh so a similar device used to harvest your whole field would consume about 17.4kWh per acre making this another negligible energy cost.
By maintaining ideal grow conditions, you should be able to grow about 37 bushels of wheat in about 6 months, which will yield a total of about 1550 pounds of flour after processing. This gives you a cost of about 5,756,600 kWh or 3814 kWh/lb of flour. Your civilization better have some pretty cheap power though or this flour is going to cost you hundreds of dollars a pound to grow.
Since you mentioned in comments that this is an archaeology the size of Connecticut, you have a total area per story of 3,548,427 acres which will meet the annual wheat consumption at current demand for about 30.5 million people per floor at a cost of 2.04e13 kWh per floor per 6 month growing cycle. This is about 10 times the United State's entire energy budget in 2019.
As a final suggestion: vertical farming is already horribly inefficient, and wheat is a particularly bad crop to do it with. If you need more room to grow your wheat it might be better to do it on barges taking advantage of all that unused flat space we call oceans, plus it makes use of an otherwise wasted part of our planet's thermal budget so that you aren't causing massive global warming by generating thermal energy at levels that are proportionally significantly compared to direct sunlight. There might also be some other creative scifi solutions like growing grains without the plants (sort of the same concept as growing meat without the animal) which could give you a wheat like GMO that could be 10s of times as efficient both per acre and per kWh.