It seems EAS servers are having trouble accessing sqlite3.org. Maybe it's some bad config on their server, or perhaps sqlite3.org is blocking the traffic? who knows.
This is a problem because the sqlite3 pod used by expo-sqlite (https://github.com/clemensg/sqlite3pod) downloads sqlite3's source from this domain.
I have mirrored a fork of sqlite3pod which includes the sqlite3 source archived inside the repo: https://github.com/TykeeLabs/sqlite3pod-mirror
The attached config plugin overrides the location of the sqlite3 pod in the ios project's Podfile to point at this new repo. The installation no longer fails because EAS can still access github, by necessity.