IMO, iCloud is a convoluted mess. You absolutely should be able to upload pics to iCloud and then remove them from your phone. Then again, without paying extra, you get an anemic 5gb of space on iCloud shared for everything while any modern iPhone will have 32gb, 64gb, or more of storage space on the phone itself (yes, I know other stuff uses this space as well but I'll bet for 99% of people, photos take up the most space).
I have iCloud Photo backup disabled (I use Google Photos) so I'm not sure of the settings but tap Settings, your name (to access Apple ID, etc), then iCloud, then Photos and look over the choices there.