The silicon strain-gauge effect is well-known, and has to be accounted for when mounting precision chips like voltage references. Here's one where it's clearly visible as two slots in the PCB on either side of the precision chip, to prevent board strain from being transferred up into the chip:
Further down the line... that chip has a plastic package. Plastic is hygroscopic, i.e. it will take up water. Even the minute amounts of water from the humidity in the air. This deforms the plastic, and adds additional strain to the IC.
The chip you linked is in the 3-8 ppm/°C range. Stuff in the 0.5 or 0.05ppm range like LM399/LTZ1000 are all in metal cans for that reason
(another fun fact... the LTZ1000 ultra precision reference has an output voltage of 7.0 to 7.5 Volt. It's precise, but not accurate)
https://voltagestandard.com/01%25-voltage-references