Electronic – Battery reads 5V but can’t power a 5V sensor

I think you can fix it as follows:

Put a pulldown on sysoff, maybe 100k. Just make sure it is strong enough to overpower the internal 5M pullup. Also keep sysoff connected to your IO expander. It should be configured as an output driven low. But when you want to power down, have the expander drive the output high, which will overpower the 100k pulldown, and turn the system off.

Once the system is off, your rails will all collapse, so the IO expander will be dead, and the 100k pulldown will ensure that sysoff is now low so that startup will be possible the next time charger is attached. You will need to make sure that the IO never goes high during bootup or normal operation. For example, program it to be low before you program it to be an output.

These problems are hard to diagnose. The first thing I would do is swap the level and pressure ADC inputs to make sure that there isn't some sort of software issue. Even if you've looked at the code a thousand times I would do this.

The impedance of your sensor is pretty high to feed directly to the ADC input. I think you should add a unity gain, non-inverting buffer between the sensor and the ADC input.

Bypass capacitors may be needed. There's not enough information to tell where they should be added or what their values should be. I would be sure to bypass the 5V supply for the sensor. You could add a small capacitor to the output of the sensor as well, assuming that the pressure is not changing rapidly.

You could also try slowing the ADC clock rate to give the sample-and-hold more time to charge. Sometimes putting the processor to sleep during a conversion can reduce noise as well.