I checked to see which version was installed on my GrapheneOS (Pixel 7) phone. It has version 137 installed currently. I poked around to see if I could update it, couldn't figure out how. I saw that in App Store -> ... -> Settings -> Auto-Update apps was set to Enabled, and the Update interval was set to 6 hours.

I changed the Update check interval to 1 hour. I'll try to revisit this in an hour to see if the version of GmsCompatConfig was successfully updated from 137 to 138 and report back here.