If ip link does not show the wifi interface either you need a different kernel or the board has been physically damaged. If the exact same card works in another model 4 then the problem is not the kernel.
The heat problem and the system log errors are consistent from this (defunct hardware). There maybe a slim chance that the chip is busted in such a way ...
The best solution of your problem is using a High discharge Li-po battery cluster(12V) with a 5V-10A BEC. In this way you can get the power to run two pi's efficiently and without any throttle. But you need a powerful battery if you want to use it some more time without charging it now and then.
A single battery doesn't have that much discharge rate.
I'm assuming the battery is inserted in the PiJuice HAT on one Pi.
That means that Pi will have a 5V supply at the 5V power rail. You can use that to power the other Pi by connecting the grounds of both Pis and one or more of the 5V pins on both Pis.
The only question is would the 5V supply be enough to run the other Pi. As you haven't mentioned the Pi ...
wiringPi pull-ups and pull-downs do not work on the Pi4B. The ways the pulls work has changed in the new BCM2711 SoC used in the Pi4B.
See this question.
As far as I know they do work correctly on the Pi3B (but I have not tested recently).
A raspberry pi need 5 volts to operate. So use a voltage regulator . It is best to use the official PSU though. But a 2 A power source is good. You can use the BEC(that is a very good idea). But keep the voltage regulation as low as possible(Assuming you are using an inverter)
Unfortunately this is normal.
The original Raspberry Pi Model A and B used a linear voltage regulator to step down from 5V to all the lower voltages it requires for its operation.
Its advantage is that it has a pretty smooth and steady output voltage. But the down side is that the excess voltage is literally being burned. (e.g. a 3.3V linear voltage ...
There is extensive documentation on the revision field from /proc/cpuinfo on raspberrypi.org nowadays:
This documents both an older (incremental) revision code (values 0x0001 to 0x0015, used for the original Rpi 1 models), and a newer format (introduced with the Rpi 2) ...