Systemd doesn't seem to respect After= dependency?

I have a PostgreSQL server (postgresql.service) and a basic shell script (mobilizon-postgresql.service that is run to provide some assertions on the database to a third service (Mobilizon).

So naturally, mobilizon-postgresql.service is configured with an After= dependency for postgresql.service:

# systemctl show mobilizon-postgresql.service | grep After=
After=basic.target system.slice systemd-journald.socket sysinit.target postgresql.service

Though after a reconfiguration of the system (which didn't touch these dependencies), I'm seeing the following behaviour in the logs:

1677672119.103035 myserver systemd[1]: Starting Mobilizon PostgreSQL setup...
...
1677672119.153192 myserver systemd[1]: Starting PostgreSQL Server...

So, mobilizon-postgresql.service is started before the startup of postgresql.service.

1677672119.279742 myserver mobilizon-postgresql-start[329444]: psql: error: could not connect to server: No such file or directory
1677672119.279742 myserver mobilizon-postgresql-start[329444]:         Is the server running locally and accepting
1677672119.279742 myserver mobilizon-postgresql-start[329444]:         connections on Unix domain socket "/run/postgresql/.s.PGSQL.543>
1677672119.283558 myserver systemd[1]: mobilizon-postgresql.service: Main process exited, code=exited, status=2/INVALIDARGUMENT
1677672119.283707 myserver systemd[1]: mobilizon-postgresql.service: Failed with result 'exit-code'.
1677672119.289678 myserver systemd[1]: Failed to start Mobilizon PostgreSQL setup.

So of course, mobilizon.postgresql can't setup a connection to the db.

1677672119.503881 myserver postgres[329458]: [329458] LOG:  starting PostgreSQL 13.10 on x86_64-pc-linux-gnu, compiled by gcc (GCC) 11>
1677672119.512541 myserver postgres[329458]: [329458] LOG:  listening on IPv4 address "0.0.0.0", port 5432
1677672119.512863 myserver postgres[329458]: [329458] LOG:  listening on IPv6 address "::", port 5432
1677672119.519498 myserver postgres[329458]: [329458] LOG:  listening on Unix socket "/run/postgresql/.s.PGSQL.5432"
...
1677672119.871989 myserver systemd[1]: Started PostgreSQL Server.

Only later the postgresql.service is reported to be fully started.

This behaviour goes completely against my understanding of After=. From systemd.unit(5):

If unit foo.service contains the setting Before=bar.service and both units are being started, bar.service's start-up is delayed until foo.service has finished starting up.

Am I having wrong assumptions here?

Systemd version is 251.12, Distro is NixOS 22.11

What does systemd mean by "finished starting up"? man systemd.unit says

for service units start-up is considered completed for the purpose of Before=/After= when all its configured start-up commands have been invoked and they either failed or reported start-up success.

So you need to look in the postgresql service file to see if it is doing something like forking and putting its pid in a file, or using sd_notify() in its code to signal "ready". It's not very useful.

Sadly, the easy way round this is to make the mobilizon-postgresql service wait for the Unix domain socket to exist, using inotifywait or similar, or add Restart=on-failure and RestartSec=1 to retry until success.

Systemd's idea of how things should work is that you create a socket unit, and whenever anyone tries to open that socket, you launch a program. In this case, by starting your script, which opens the socket, it launches postgresql.