How to buy more iCloud space ?

Correct. iCloud is not a hard drive in the sky. To save space you have to turn on optimization. See optimization specifically with reference to "Set up and use iCloud Photos" - https://support.apple.com/HT204264

--> Save space on your device

iCloud Photos keeps all your photos and videos in their original, high-resolution version so only smaller versions are on your device, but they will still take up some space.

Click on this link to discover how to "Upgrade your iCloud storage plan" --> https://support.apple.com/HT201318

I don’t pretend to understand it fully myself... but I did just want to point out, that I upgraded to more iCloud space, and it apparently does nothing to minimize the storage used up on your devices! In fact, if you delete a photo on a device, it automatically also gets removed from the iCloud. So the only use I can see for this service is that it does retain a copy of everything on the device for a period of time so that you can restore them onto devices if needed. That’s just not what I need...I need somewhere else to safely keep them indefinitely.

Not sure if this helped, hope so.

you can buy a mini flash drive like SanDisc iXpand, this fits right into the phone and backs up the photos just like iCloud, but you can also copy and keep the photos on there or transfer them anywhere you’d like.