As a general comment, If the ac system is fully charged, then the high (over) pressure and low (under) pressure sensors won’t see problems so will allow the compressor to kick in if it’s commanded to do so by the ac control (hvac?) module.
Basically, ac pressure switches are used to protect the ac system from over pressure and under pressure conditions that can damage the compressor and/or other components.
For the compressor to kick in, it requires that it is commanded to do so by the control module and the pressure interlock feature not to inhibit the compressor from starting … that means means the controlling module must be getting the correct signals (inputs) so it can command the appropriate signals (outputs) …
So as some VE’s had both a pulley clutch as well as a variable volume compressor, those types need wiring to activate the clutch pulley (so the compressor can be turned by the engine) and wiring for the PWM solenoid (so that the compressor volume can be controlled).
Basically have a look at the compressor to see that all plugs are indeed connected and there are no loose connectors floating about the vicinity. Hopefully the ac compressor wasn’t changed with the engine and the correct type is fitted so it’s just a forgotten plug that wasn’t pushed home.
Oh, and if the ac was working before the engine swap, it’s an issue for the mechanic who did the engine swap to sort out. Could be pinched wire, squashed ac line or anything really.
As a last comment Adairs is (was) a great resource for ac related technical bulletins but the link I had doesn’t work any longer
Another great resource is the ve commodore factory workshop pdf manual that is floating about the www (a link can be found within JC’s) and that manual has all the specifics you’d need