IIRC, there was some model of automobile (a Honda, I think) that had this same problem on a larger scale; the tires installed at the factory tended to create a big static charge on the car and it’s passengers as it rolled down the road, and as a result, toll booth operators came to dread the approach of said model car. The solution for the auto maker was to use tires with a different rubber compound in them. I imagine that getting different tires for your chair could be tougher, though.
Maybe you could get or improvise some sort of grounding strap - a thin metal chain, attached to the metal frame of your chair, that drags on the floor at all times. Semi trailers that carry flamable fluids like gasoline often have such a chain, for the same reason. Since you have carpet in your office though, this might not work, although it can’t hurt to try.
Maybe the carpet could be treated with different (anti-static) chemicals when it’s cleaned.
Maybe there’s some anti-static treatment for the tires.
Or who knows, maybe you CAN get different tires - I don’t know wheelchairs from a hole in the ground.
Maybe it’s not the wheels-on-carpet friction that causes the static buildup; maybe it’s the cloth-on-cloth friction of your clothes on the chair. That’s the case with my chair at work, which gives me quite a charge from the least little shifting. In that case, some anti-static laundry spray on the seat and back of the chair could make a difference, at least for a little while. I know people who have this problem with their cars’ seats, and the spray fixes the problem for a few days.
Before mucking about with the insides of a computer (which is a really bad place to have a static shock), I generally touch a faucet or some other ground with a key or a coin. The spark jumps from metal to metal, and unless the spark is quite a doozy, I can’t even feel it. Maybe as a last resort you could carry a metal pen (something you need in the office anyhow) with you, and touch grounded things with the pen first.
Maybe someone else can offer something more specific.