Downloaded the PostgresSQL 13.7 and followed the instructions.
Postgres 13.7 is running, but the EM can't connect to it.
If stop I PostgreSQL 13.7 and start the PostgreSQL 9.6 , the EM connects just fine to PostgreSQL 9.6
Release : 10.7.0
Component : Introscope
Unsupported / Compatibility
APM 10.7 .x supports PostgreSQl 9.6.2.
APM 10.8 supports PostgreSQL 9.6.2, 11, and 13.4,13.6,13.7.
Please refer the updated compatibility guides .
The APM 10.8 Guide lists Postgres 13.8.
The 13.8 was a typo and the Compatibility Guide was updated.