I studied this very topic for the Space Shuttle program and NASA's Commercial Resupply Services and included my findings in a paper published last year.
Sending cargo and crew to the ISS involves sending a vehicle that is designed to safely reenter with cargo and crew. As much of the mass-to-orbit is used for this vehicle, the amount of payload delivered to the ISS is much smaller than the total mass launched to LEO orbit. Therefore, the cost-per-kg of payload to the ISS will be higher than the cost-per-kg to orbit for a system that only launches satellites and does not involve sending a vehicle to orbit as well.
To arrive at a cost-versus-year trend for the Space Shuttle I assumed that all Space Shuttle missions were ISS missions, and then plotted the total amount of payload delivered versus the amount of money that was spent on the program, using 2023 inflation-adjusted dollars.

This approach gives us the plot shown above in Figure 3. By fitting a curve to the data in Figure 3 and plotting the inverse slope of that curve versus time, we end up with the orange curve of a USD-per-kg versus year shown in
Figure 2.

We can see that the Space Shuttle’s cost-per-kg came down over time, but we can also see that there are a few peaks and valleys in the curve. The peaks were caused by the Challenger and Columbia disasters. Between these
events, cost dipped to as low as 59,000 USD/kg.
If we apply the same methodology to Commercial ISS resupply services in general (blue curve) and the cost with the market leader, SpaceX (purple curve), using data from usaspending.gov, we observe that in practice the costs have only recently managed to achieve cost parity with the Space Shuttle Program.
An Aug 2018 independent audit from the Office of Inspector General, on page 27, projected that the cost of commercial ISS resupply with
SpaceX would be 71,800 USD/kg, which aligns well with the usaspending.gov data shown in Figure 2.
Other corroborating data includes an Aug 31st, 2022 press release by NASA where they announced that they had awarded five additional missions to SpaceX at a cost of $\$$1.436 billion or $\$$287 million per mission. This places
the cost of future resupply missions 10 through 14 at 1,436,438,446 USD, which works out to 86,794 USD/kg if we assume that each mission delivers the maximum payload of 3307kg to the ISS.
On March 8th, 2023, Robyn Gatens, Director of the International Space Station at NASA, stated informally during a Q&A session at the IEEE Aerospace Conference that half of the ISS budget
goes to launch costs. As NASA spends roughly 3B per year on the ISS, and resupply runs deliver people and cargo at a rate of roughly 20,000kg per year, this works out to...
$$3,000,000,000 USD / 2 / 20,000kg = 75,000 USD/kg$$
Of the four sources referenced, the 2018 Office of Inspector General forecast was the lowest at 71,800 USD/kg. NASA's 2022 press release was the highest at 86,794 USD/kg.
(Note: the press release cost assumes that Crew Dragon Capsules are always filled to their maximum rated payload capacity of 3307 kg - which may not be the case for every mission.)