Do I need to upgrade storage on my iPhone if I already have iCloud set up on my Macbook

I have 200gb of storage on my Macbook. I recently got an iPhone for the first time and I linked my iCloud account. Now the phone is telling me the 5gb of storage is full and it's asking me to upgrade my storage. Why isn't it recognizing my current iCloud plan? It has my iCloud info already. Do I need to set up a separate monthly storage backup for my phone and my Macbook? I'm very co