Unknown song from Gakkou Gurashi
I was looking for the same track as you when I heard it on air! The music was composed by MOSAIC.WAV and the OST was finally released a few weeks ago.
The track you're looking for is no. 15: 優しいめぐねえありがとう (Yasashii Megu-nee Arigatou)

There are a few other tracks I wish made it on, but they're going to release a 2nd volume on November 26.