Are two of the A/C relay terminals supposed to be hot when car is in off position, or one terminal hot (battery voltage) and one cold?

Okay, terminal 29 takes power from the relay to the A/C clutch. Terminal 28 is constant power from fuse 22. Terminal 30 is the relay control signal from the PCM. Terminal 31 runs on power that comes from fuse 22 as well and from there through the A/C pressure switch, if the is a refrigerant charge in the system that switch should be closed. So, you should have power at terminal 28 and 31. As they get power from the same fuse. Follow the highlighted path.

I dug around a bit and found an error in the diagrams. Fuse 22 should be switched power So both pins 28 and 31 should have power only when the key is on. If you jumper 28 and 29 and the compressor works, I would check for switched power at terminal 31. That should have power at the same time as 28. If it doesn't go, find the pressure switch and jump between pins 1 and 2 in its connector. Do you have power at 31 now? If yes, the pressure switch is bad. If you do have power at terminal 31 but still no A/C then check if pin 30 shows a ground when the A/C is selected on at the control panel. If it doesn't then there may be a problem in the blue wire w orange stripe.

Sounds like the power side is okay and it has some charge because if the system was empty, it would drop the power at terminal 31 as the pressure switch would open. So now you need to determine if the ECM is the issue. With the readings you had from testing, pull the A/C relay and use a test light connected to battery power. Turn the A/C on max cold and touch pin 30 in the relay socket. If the light comes on the ECM is switching properly, if it doesn't and your earlier test showed it has continuity then we need to verify the powers and grounds for the ECM. Attached are the diagrams for those grounds.

So, pin 35 in B136 is a floating ground that goes to joint connector A and if it fails you will know it, the car wouldn't start or run.
So, you show continuity between 30 and the ECM but the ECM won't activate the A/C.
A couple more things to look at. There are two sensors (ambient air and interior air temp) that can tell the ECM not to run the /AC. Basically, those can tell the ECM that it's already colder than the temperature selected and not to run the A/C. The first two are the interior, it's in the dash next to the center stack. It can get clogged with crud or just fail. Testing it involves gaining access to it or to the AC control module behind the right side dash. To access it you remove the side panel of the console, and the sensor and connector are right there. Testing is simple, it's a thermistor with the attached temperature curve. Simply measure the resistance across the pins. An even faster way would be to use a scan tool to access the A/C module and see what it reports as the ambient and interior temperatures. For the ambient temperature sensor, it is mounted behind the front bumper, if your car shows external air temperature and it's close to actual temperature then it should be okay.
These two can stop the A/C if you selected say 72 degrees but the interior sensor was disconnected with it an open circuit it will max out and show -40C as the temperature! Probably don't need A/C at that temperature. Ambient would show the same.

Look at the diagram I attached above find the module and connector B282, in it are pins 5 (white with green) and 15 (blue) and measure the resistance between them. Compare that to the temperature curve above. So, say you measure 5200 ohms and it's 75 degrees out, the sensor is bad. Measure 1250-1275 ohms at 70 and it should be okay.
The issue then becomes that if the sensors test okay and the system pressures are enough that it should work but isn't then you will need a scan tool that can control the ECM and the A/C module, which would be the only way to determine which module isn't activating the A/C.

No rush. Oh, does everything else appear to be operating okay and it's just the A/C that doesn't? If so, I would sort of suspect the controller more than the ECM but without digging in with a scan tool and scope, I can't say that with 100% authority.

More data makes it easier in most cases. The signal wire staying at battery voltage means the ECM either isn't getting the signal to turn on the clutch, is being told not to, or it cannot internally. That is the question now. Which of the three is it. If you were to jumper that pin to ground the AC should function, but without any control. By testing the aspirator and ambient temperature you eliminated those, you already know the compressor will turn on and cool as well. That leaves the ECM and the control head. Both which communicate on the CAN to transfer that data. This would be when a scan tool would help, if you turn the A/C on and the scan tool shows that the ECM received that data, but the relay stays off, it's a bad driver in the ECM. If you turn it on but the ECM doesn't show it, it's likely the control head.
Now if you had a 94 or even 2004 version of this it would be much easier, they didn't stick everything in a module and make it hard to test.

That Evap sensor tells the control head if the core freezes up. The 1.2K sounds about right for the resistance.
Pin 6 at the ECM is a simple voltage trigger key on it should be around ground with the A/C on, battery voltage with the A/C off. Here are the tests for the ECM with the 2 for A/C control highlighted. The info I have doesn't do this for the A/C module.