I was able to SSH into a GitHub runner using tmate. After playing around a bit, I realized a bunch of time and disk space was spent installing the Android NDK.
React Native 0.70 uses uses an ancient version of the Android NDK (21.4.7075529) that is no longer preinstalled on GitHub runner images. As a result, the Gradle build has to install that Android NDK. During installation a large amount of disk space is used (about 5 GB or so), which is later partially freed after the installation succeeds.
In fact the GitHub runner comes with 4 NDKs preinstalled. They take up a lot of disk space. This diff deletes the NDKs that we don't use. (Actually it keeps 24 around because React Native 0.70 mentions two NDKs... 24 for Apple silicon and ancient 21 for the rest.)
Worth noting that React Native 0.71 and 0.72 move to using NDK 23 (for both Apple silicon and other), and 0.73 moves to NDK 25 (fairly recent). As a result we hopefully won't need to download an NDK during GitHub CI build in the future.