iPhone won’t backup says not enough storage but have 32g available

Where are you backing up your device? Is it on iCloud? Have you purchased iCloud Storage?

When you get a popup message on your iPhone or iPad that the storage is full.

Look closely into the storage of the iPhone and iCloud.

iCloud storage is primarily for keeping a copy of your iPhone data safely on the cloud. If you delete data on iPhone, data on iCloud is gone too.

Turn iCloud features on or off

1. On your iPhone, iPad or iPod touch, go to Settings > [your name] > iCloud.
2. Turn iCloud features on or off.

Turn iCloud features on or off - Apple Support

iPhone Storage (Setting > General > iPhone Storage)

1. Total storage remains the same throughout the lifespan of the iPhone
2. Storage can not be enhanced
3. You may take back up on Mac or PC using iTunes without iCloud

iCloud Storage (Settings > [Tap your name] > iCloud)

1. By default, every user gets 5GB of free storage space
2. You can buy more storage based on your requirement of 50, 200GB, and 2TB with a monthly subscription
3. Based on your storage capacity you can back up your iPhone or iPad
4. Space can be shared between your family members for a storage plan beyond 200GB