There is no way to add device storage space, it is fixed on your iPhone and when purchasing the phone you decide how much storage space you want. Purchasing an iCloud subscription helps with device storage for Photos when you use the Optimized Storage option on your device along with iCloud Photos. This saves the high resolution photos/videos in iCloud while only using the device storage for the smaller thumbnails. To view the photo in high resolution for editing or printing, it will have to be downloaded from iCloud into your device storage and space on your device will have to be available for you to do that. Other things like apps are only stored on your device, so iCloud storage will not let you download more apps.
In addition, if your backup file is larger than 5GB, you will need to purchase an iCloud+ plan if you want to continue and backup your phone to iCloud.
Bottom line is that Device Storage and iCloud Storage are 2 different things. These 2 support articles will help with managing both Device storage and iCloud storage:
How to check the storage on your iPhone and iPad - Apple Support
Manage your iCloud storage - Apple Support