You're not wrong. The confusion arises because we're comparing apples and oranges - headspace equilibrium pressure for a given level of carbonation vs behaviour of gas at different temperatures. The two physical phenomena don't react to temperature changes in the same way. Furthermore, the carbonation level takes hours or days to settle on a final value, while the drop in pressure proportional to temperature takes place more or less instantaneously - I think it's this second point that's causing some confusion.

If you take a beer that has sat at 12 PSI at 20C for long enough to reach equilibrium then yes, it will be carbonated to 1.5 volumes.

If you cold-crash it the equilibrium changes, but the total amount of gas in the container does not

For argument's sake, let's imagine a 27L FermZilla with 20L of beer and 7L headspace which has been spunded at 12 PSI @ 21C, and let's round the resulting 1.49 volumes CO2 to 3g/L

So in total the container has:

3g/L * 20L = 60g dissolved CO2

+ 7L @ 26.7 psia @ 294.15K CO2 = 0.5269 moles = 23.2g CO2 gas

= 83.2g total CO2

Now let's cold-crash that to 2C / 275.15K

If we could crash-chill instantly, then in that instant we'd still have 3g/L = 60g dissolved CO2 in the beer, and we'd have headspace pressure of

26.7 psia * (275.15 K / 294.15 K ) = 25 psia = 10.3 psig , so that's our upper bound on pressure and lower bound on carbonation.

Conversely, if all the CO2 dissolved in the beer (0 psi absolute, or -14.7 psi gauge!) you'd have 83.2 / 20 = 4.16g/L ~= 2.08 volumes CO2, so there's the upper bound on carbonation and lower bound on pressure.

The equilibrium must exist between those figures. The relevant part of the Carbonation chart:

View attachment 118310
Where those values at 2C are for pressures of 0-6 psi gauge.

Using the equations we can work out what the headspace pressure would be for any level of dissolved CO2. So I pulled out Excel and did that, and here's the relevant region:

View attachment 118309
At 1.72 vols, the chart says 2 psi, and I calculate we only have enough CO2 for 0.8 psi in the headspace, so it's not quite that high.

Conversely, to get down to 1 psi in the headspace I calculate the beer would have to have dissolved 1.71 vols, a bit more than the 1.62 vols indicated by the chart as the equilibrium for that pressure.

Thus we know the true value exists in between those pairs of figures - between 1-2 psi and 1.69 - 1.72 volumes of CO2

So you're absolutely correct - on a long enough time scale, you'd expect a fermenter cold-crashed from 12 psi at 21C down to 2C to settle a bit below 2 psi.

Conversely, on a short timescale I'd expect a fermenter just recently crashed from 12 psi at 21C down to 2C to be reading a bit less than 10 psi, gradually approaching 2 psi over several more days.

I really hope that's helpful because it took ages to write up.