Thank you for the -h option.
I found another way to see it:
# netstat -pantu
tcp6 :::389 :::* LISTEN 687/slapd
Just for information for people who pass by this post:
There is nothing to do with ipv6 in openldap.
Like you say it anomie, "By default, it listens on all addresses.".
What means that the type of connection (ipv4 or ipv6) to search the information in the database depends of the consumer.
If the consumer speaks ipv4, the server will answer it ipv4.
If the consumer speaks ipv6, the server will answer it ipv6.
Don't look farther.
If you want to slapd listen specifically on a type of network (man 8 slapd):
-4 Listen on ipv4 addresses only
-6 Listen on ipv6 addresses only
It's important to read the "schemas" to understand the format and how to implement/integrate informations into the database of openldap.
And, if there is no way to implement ipv6 informations, contact the author of the schema.
Have a nice day