How to disable iCloud storage of photos? I would like to use iCloud only for pictures synchronization, but not for storage (Privacy concerns + too large pictures library - I don't know if Apple's security for pictures storage is that good, plus no desire to pay for additional iCloud storage.). 

Currently, most pictures appear to be stored locally on the MBP (not in iCloud), though new pictures snapped on iOS do appear in this list (not reliably, though).

The requirements:


All the iOS devices should show the complete library, and only
download a larger resolution picture on-demand, so as to always keep the maximum amount of storage available.
A picture snapped using any iOS device must be synced to all
other devices, without waiting for a manual synchronization through iTunes.
Only MacBook Pro should be storing the full, high-resolution
pictures and videos locally, but I wouldn't mind if the MacBook also had one. Just wanted to avoid having this older computer having to periodically download such a large amount of data.


The setup:
iOS devices:


iPhone 3GS, iOS 6.1.3
iPhone 5c, iOS 10.3.3
iPad 2, iOS 9.3.5
iPhone 6, iOS 12


Macs: 


MacBook, Mac OS OX 10.11.6
MacBook Pro, Mac OS X 10.11.6


NASes:


Synology NAS for backups. HDD-based, it's noisy, so not usually
powered on. I would prefer not to leave it open to the Internet for security reasons.
LaCie Cloudbox, fvdw-sl firmware. Usually powered on. Can take
OwnCloud / NextCloud, but seems too low-powered for this purpose.


Others: 


LibreELEC media player based on Raspberry Pi 3. Currently stores a
local copy of iTunes songs on an external SSD. Issue: since it's only
100Mbps connectivity, it is painfully slow to list all files.
Shared web hosting with NextCloud installed.


How do I achieve this goal, considering my setup?
For some reason Apple's terminology in regards to iCloud settings for photos isn't crystal clear to me.

Edited for clarity
IMHO, you can't accomplish this.

You're describing iCloud Photo Library, except you don't want to use iCloud Photo Library or iCloud storage.

Consider requirement #1: in order for all iOS devices to have access to the complete library, it has to be somewhere that's permanently available. The MacBook Pro can't be the answer to that requirement, because if you're away, the MBP will either be on a different network and/or be asleep. Or rebooting. Or updating. The only resource that's always available is online. This is why iCloud Photo Library stores the complete library in iCloud storage.

Consider requirement #2: in order to sync, each picture must be uploaded to a readily available resource and then each device needs to be alerted to that fact and download it. Again, this is exactly what iCloud Photo Library and/or PhotoStream do.

Here's what I do, which might help. I also have multiple Macs and iOS devices. All of them use my Apple ID and I have turned off iCloud Photo Library, but turned on PhotoStream. I have personally designated one of my Macs as the Master Photo Library (MPL). Any pictures I take with any device automatically show up in my MPL. Those pictures are also available on other iOS devices within the limits of PhotoStream (PhotoStream only keeps the last 30 days and a max of 1000 photos). Once a picture is no longer in the PhotoStream (31 days later, or 1001 photos later), the picture is still available on the device that took the picture, but, it's also permanently saved in my MPL.

Videos are of course another thing. It's called PhotoStream, after all. So, every time I take videos I care about, I connect the iOS device with a cable to the MPL and offload them.

This does not accomplish exactly what you want, but it gets very close. It's the best answer I can come up with. The only thing "better" is using iCloud Photo Library, which I don't use only because of the monthly cost, not because of security.