Summary: You've got the two resistors in the feedback voltage divider (setting the output voltage) reversed on your schematic compared to the desired values, and presumably also on your PCB.
It's the lower resistor in the feedback voltage divider (R101 on your schematic, R1 on the typical application schematic in the datasheet) which should be 15 kΩ. However you've got that value as the upper resistor (R102 on your schematic).
This is what the relevant part of your original schematic shows:
Here is what your feedback voltage divider resistors should look like, adapted from the typical application circuit in the MAX38909 datasheet:
Notice how the upper & lower resistor values are reversed compared to your schematic. With the resistor values shown in my version, you should indeed get your desired 3.82 V.
For those who want to do the calculation, here is the relevant paragraph in the datasheet:
We can also see in this table of various example output voltages from the datasheet, for an output voltage of 3.82 V, then the lower resistor (R101 on your schematic, R1 on the datasheet schematic) should be 15 kΩ and the upper resistor (R102 on your schematic, R2 on the datasheet schematic) will be between 75.0 kΩ (which would give a 3.6 V output voltage) and 97.6 kΩ (which would give a 4.5 V output voltage). So that also confirms that your 80.6 kΩ as the upper resistor in the feedback voltage divider, will give an output voltage between those two voltages:
A quick calculation suggests to me that with your existing feedback voltage divider resistor values (15 kΩ for the upper resistor and 80.6 kΩ for the lower resistor) the output would be around 0.7 V, which matches what you report.