My iPhone says storage space = 32 GB

You're buying iCloud storage space, not phone storage. You can't increase the storage on your phone, it is a fixed size.

The difference between phone storage and iCloud storage -

https://support.apple.com/en-us/HT206504

Here are some helpful articles that can guide you on how to free up storage space on your phone.

How to check the storage on your iPhone, iPad, and iPod touch

https://support.apple.com/en-us/HT201656

Manage your photo and video storage

https://support.apple.com/en-us/HT205703

Clear Other storage on your iPhone or iPad

https://support.apple.com/en-us/HT211686

You will have more room to backup your phone. If you don't need it, you can always cancel the subscription.

You're welcome.