Go back to basics. From the example you quote, full scale input voltage range is about 10V. This represents the differential range +/-5V, with +5V giving 7FFFFF, 0V gives 000000, and -5V gives 800000.
Each step is therefore 10/2^24 = 0.6uV.
You need to get a very stable reference voltage, derived from a stable regulated supply independent of any other load.
So run a 3V3 regulator from the Pi's 5V supply, add a high quality capacitor, then add a precision voltage regulator, one specified to sub-microvolt stability.
The absolute accuracy implied by 24 bits can only be achieved by calibration against a suitable voltage standard.
Noise will be a problem. You will need to decouple all your supplies, again making them independent of other loads. Everything will need to be screened very effectively.
Read the datasheet and the application notes for ideas about how to make it all work.
Last, but not least: What are you measuring that requires 24 bit accuracy? Are you being realistic about what you can achieve? How many bits are actually significant in your application?