Though SJC Airport does not currently offer a sensory room and/or other Special Needs specific resource area, it does offer nursing area(s) near Gates 8, 18, 21, 24 & 26. [1]. These rooms may offer a more low stimulation area than in the main terminal; TravelingWiki Foundation defers to the Airport as to the access requirements for nursing areas if not using those areas for nursing activity.
Photo at Top of Page: https://upgradedpoints.com/travel/airports/norman-y-mineta-san-jose-international-sjc-airport/
Photo of Nursing Room: https://www.flysanjose.com/amenities/nursing-room