If you have upgraded iCloud storage and are seeing a message on your device that storage is full then it is possible you are not making the best use of iCloud storage and need to use optimization features. If you do have optimization activated then it is possible you are exceeding your device's needs in terms of on-device storage and you need to buy a device with more storage.
Click on the link to learn how to optimize the storage on a device --> "How to check the storage on your iPhone, iPad, and iPod touch" - How to check the storage on your iPhone and iPad - Apple Support
- "If your device is low on storage, it automatically frees up space while installing an app, updating iOS or iPadOS, downloading music, recording videos, and more.
To make more storage available, your device can remove some of your items, like streamed music and videos, files in iCloud Drive, and parts of apps that aren't needed. It also removes temporary files and clears the cache on your device. But your device only removes items that can be downloaded again or that aren't needed anymore."
Here's the same information as a video: "How to free up space on your iPhone, iPad, or iPod" - https://youtu.be/bnhuHSv_WrI
Optimization specifically with reference to "Set up and use iCloud Photos" - Set up and use iCloud Photos - Apple Support
--> Save space on your device
iCloud Photos keeps all your photos and videos in their original, high-resolution version. You can save space on your device when you turn on Optimize Storage.
Manage your photo and video storage - "Learn how photos and videos use your iPhone, iPad, and iPod touch storage, ways to save space, and how to upgrade your iCloud storage if you’re running out."
Manage your photo and video storage - Apple Support
You say "backup safely". For me the only truly safe way is to back them up on multiple hard drives at home. In fact even Apple provides this information:
Legal - iCloud - Apple
M. Backup
iCloud Backup periodically creates automatic backups for iOS devices, when the device is screen locked, connected to a power source, and connected to the Internet via a Wi-Fi network. If a device has not backed up to iCloud for a period of one hundred and eighty (180) days, Apple reserves the right to delete any backups associated with that device. Backup may include device settings, device characteristics, photos and videos, documents, your messages, ringtones, Health app data and other app data. For additional information, please go to https://support.apple.com/en-us/HT207428. The following content is not included in your iCloud backup: content purchased from the iTunes Store, App Store, or Apple Books, media synced from your computer, and your photo library if you have enabled iCloud Photo Library. Apple shall use reasonable skill and due care in providing the Service, but, TO THE GREATEST EXTENT PERMISSIBLE BY APPLICABLE LAW, APPLE DOES NOT GUARANTEE OR WARRANT THAT ANY CONTENT YOU MAY STORE OR ACCESS THROUGH THE SERVICE WILL NOT BE SUBJECT TO INADVERTENT DAMAGE, CORRUPTION, LOSS, OR REMOVAL IN ACCORDANCE WITH THE TERMS OF THIS AGREEMENT, AND APPLE SHALL NOT BE RESPONSIBLE SHOULD SUCH DAMAGE, CORRUPTION, LOSS, OR REMOVAL OCCUR. It is your responsibility to maintain appropriate alternate backup of your information and data.
iCloud storage is a convenience but when it comes down to it, you need to take on ultimate responsibility for ensuring your files are available when you want them.