Postgres replication, even in synchronous mode, does not maintain its consistency guarantees during network partitions. It's not a CP system - I don't think it would actually pass a Jepsen test suite in a multi-node setup[1]. No amount of tooling can fix this without a consensus mechanism for transactions.

Same with MySQL and many other "traditional" databases. It tends to work out because these failures are rare and you can get pretty close with external leader election and fencing, but Postgres is NOT easy (likely impossible) to operate as a CP system according to the CAP theorem.

There are various attempts at fixing this (Yugabyte, Neon, Cockroach, TiDB, ...) which all come with various downsides.

[1]: Someone tried it with Patroni and failed miserably, https://www.binwang.me/2024-12-02-PostgreSQL-High-Availabili...