My LDAP server is installed on a Proxmox container using the TurnKey
Linux template. I always thought it was a clean Debian installation. I
tried it on a fresh Debian installation, and both olcAccess and the LDAP
tree differ significantly from what is provided in the template.

I need to practice olcAccess permissions.

Maybe forget about the debian/distro stuff, if you are working with containers anyway. If you use alpine your openldap docker image is (without db) 16MB. My image with el7 was already 305MB.
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Proxmox is based on debian and is using LXC containers . But anyway the default ldap install contains only the configuration database, all other databases and organizational units ( and olc's ) are to be added by the admin.

I have some containers with no databases or large files (like proxy or vpn ) on proxmox  with 8G disks - using ubuntu ( not my choice :) ) . So the distribution is not so important. and when you talk about few gigs it's peanuts ...