After installing a new outside AC compressor the voltage at any outlet drops from 123.9 to 122.4 whenever the AC starts. This causes a momentary flicker in the household lights about 80% of the time. The AC company has installed a hard start capacitor with no change in the flicker. I had the utility company come out and they checked the voltage across the meter and saw the same thing. They said it is OK and within their specifications. Are they giving me a straight answer?

I believe they can give you plus or minus 10% of nominal. So, If nominal is 120V then the math looks like 108-132V. How big is the service, how bid is the compressor?
It might also be an undersized service or service conductors. Have you completed a demand calc for this new load with the existing arrangement?

Sounds like superb voltage regulation. ANSI limits are ~110-127, and these numbers are in most utility and appliance manufacturer boilerplate.

Incandescent lamp flicker can be very difficult to subvert, for the human eye is very sensitive to it. Looks like everything is up to snuff and then some.

Join the club, Ihave the same problem with My AC. When I had the 200 amp panel, meterbase and service entrance put in, the poco didn't bother to change the drop off the pole, so I have 2awg drops feeding a 4/0 service entrance, in the summer time when the other 2 houses on the transformer are running their ac too, I get a very pronounced flicker.
This is the ac's third season, so far so good.

Trainwire