I'll lead off with the question:
"If trying to get full resolution from the converters, what is the optimal power supply configuration when running the AD7799 from a single Li-Ion battery (2.5-4.2V)?"
I'm sort of surprised there is no app note about this specifically.
Lets say I'm using this part with a bridge type load cell as shown in the typical circuit (without that NTC thermistor part), and that it will be in use for a few hours at a time. I want to use the upper ranges of PGA gain and sample rate, which means I don't get to waste bits with supply noise:

Analog Devices AD7799
"3-Channel, Low Noise, Low Power, 24-Bit, Sigma Delta ADC with On-Chip In-Amp"
Product Page =
https://www.analog.com/en/products/ad7799.htmlData Sheet =
https://www.analog.com/media/en/technical-documentation/data-sheets/AD7798_7799.pdf
This part has three voltage requirements:
1) DVdd = 2.7-5.25V = Digital Supply for microcontroller IO interfacing.
2) AVdd = 2.7-5.25V = Analog Supply, and excites the load cell.
3) VREFIN = 0.1-AVdd = Reference voltage, recommended 2.5V.
Option 1: Power everything from 2.7V with LDOs right off the battery?
Use one LDO direct from the battery to make AVdd=2.7V, and another LDO for VRefin=2.5V.
Probably use another separate LDO to make DVdd 2.7V and also power the microcontroller with that rail?
This seems like it's the lowest noise, but wastes battery capacity (lowest the battery can be drained is 2.7V + Drop out) and it's burning power at full battery charge (4.2 - 2.7).
Option 2: Boost/Buck to make 3.3V, then down regulate from there?
Run a buck/boost regulator off the battery to make the 3.3V. Use that 3.3V to power DVdd and the micro.
The VRefin 2.5V can still be an LDO right on the battery, but where should the AVdd come from? LDO at 3V on the 3.3V rail? Just filter the hell out of the 3.3V from the buck/boost and use that for AVdd?
Option 3:
Something completely different?
The reference board for the AD7799 has really bad circuit operation descriptions and all the jumpers and configuration options make the schematic a mess:
https://www.analog.com/media/en/technical-documentation/evaluation-documentation/EVAL-AD7799.pdf This is an app note for a similar chip, AD7781, that has a better circuit with power supply filtering, but it still assumes you are starting with 5V:
https://www.chip1stop.com/pdf/liblary/tech_info/AD01/CN0108.pdf
Thoughts?