Yes, postgres has sync and async replication with the ability to even choose a quorum (so that 2 of 3 replicas confirm).

Also has logical replication now, although I wouldnt recommend it because it doesn't support DDL changes yet. Overall it's a solid db choice, but there is still some work involved.

Otherwise I'd recommend SQL Server for a fantastic commercial database that runs cross-platform and has great tooling to make everything easier and some advanced features.

In postgres you can choose if the replication is synchronous or asynchronous. For cascade replication (a slave uses as a master for another slave) the replica is always async.