PostgreSQL documentation makes it quite clear how to set up HA, I don't think you need any third-party tools other than general OS-level support for failover.
https://www.postgresql.org/docs/current/high-availability.ht...
From the official docs:
>> PostgreSQL does not provide the system software required to identify a failure on the primary and notify the standby database server. Many such tools exist and are well integrated with the operating system facilities required for successful failover, such as IP address migration. [1]
[1]https://www.postgresql.org/docs/current/warm-standby-failove...
Postgres HA is far from easy. I gave a talk 2 years ago about this (video and slides: https://aht.es/#talks-modern_postgresql_high_availability). This is an operational disadvantage.
MongoDB has built-in multi-instance sharding support. Again this is possible for PostgreSQL with table partitioning and FDW but it is hard to maintain.