PostgreSQL cluster has two primary databases after network glitch

PostgreSQL replicas never finish recovering. This is by design. Basically a replica is always in "recovering from disaster" mode except that it is using receiving the WAL segments from the master rather than on disk.

So what you are seeing is not cause for concern. If it is not working yet, then you will need to provide a more detailed description of what you are trying to do and what is not working. But as far as you are posting it seems normal.

You seem to be trying to replicate from one server to another that wasn't set up using a copy of the original server. That's why:

database system identifier differs between the primary and standby. The primary's identifier is 6022019027749040119, the standby's identifier is 6033562405193904122.

Because each newly initdb'd PostgreSQL gets a new random system identifier. When you copy an existing PostgreSQL install, it keeps the same system identifier. That's how PostgreSQL can keep track of whether one server can replay WAL from another.

You can only use physical replication if the replica is a copy (file-system level backup e.g. pg_basebackup) of the master. See the manual's detailed coverage on replication for more information.

Update:

The instructions shown above should be fine, but they're not as clear as they could be.

The standby server's data directory is supposed to be replaced by the base backup you create at step 8, if it exists in the first place.

You can't make an existing PostgreSQL instance into a standby for another without replacing its data directory. You need a copy of the master's data directory to run a standby. A common way to set that up is to take an existing standby, delete its data directory, replace it with a copy of the master's data directory, and then configure it as a replication slave. That's what I think step 8 is supposed to be doing.

Instead of doing that I think you probably used an existing data directory for the slave and tried to start it up as a replica of the master. That will not work, and will result in the errors you showed.

The main PostgreSQL documentation on replication is the recommended and primary resource for information. I suggest going there first.

You might also want to check out repmgr, which helps automate replication and failover tasks.