According to the docs, there is an option specifically for mounts:

RequiresMountsFor=/srv/file/named

ensures all mounts required to access /srv/file/named are in place before this unit starts.

This has worked for BIND. For PostgreSQL, however, there seems to be some other error. The service seems to be down (Webmin tells me it is, and the application using it does not work either), yet systemctl status postgresql tells me it’s up:

● postgresql.service - PostgreSQL RDBMS
   Loaded: loaded (/lib/systemd/system/postgresql.service; enabled; vendor preset: enabled)
   Active: active (exited) since Sun 2021-06-13 18:48:18 CEST; 4min 57s ago
  Process: 543 ExecStart=/bin/true (code=exited, status=0/SUCCESS)
 Main PID: 543 (code=exited, status=0/SUCCESS)
    Tasks: 0 (limit: 4915)
   CGroup: /system.slice/postgresql.service

According to the docs, there is an option specifically for mounts:

RequiresMountsFor=/srv/file/named

ensures all mounts required to access /srv/file/named are in place before this unit starts.

This has worked for BIND. 

For PostgreSQL, however, there seems to be some other error. The service seems to be down (Webmin tells me it is, and the application using it does not work either), yet systemctl status postgresql tells me it’s up:

● postgresql.service - PostgreSQL RDBMS
   Loaded: loaded (/lib/systemd/system/postgresql.service; enabled; vendor preset: enabled)
   Active: active (exited) since Sun 2021-06-13 18:48:18 CEST; 4min 57s ago
  Process: 543 ExecStart=/bin/true (code=exited, status=0/SUCCESS)
 Main PID: 543 (code=exited, status=0/SUCCESS)
    Tasks: 0 (limit: 4915)
   CGroup: /system.slice/postgresql.service

A look at the unit file tells me it does nothing other than running true. This seems to be a different problem than I thought I had; apparently I edited the wrong file.