I bought iCloud storage but still have no space on phone

iCloud storage does not free up space on your phone. It only frees up space you can use to store on iCloud.

The only way to reduce storage on your phone would be to offload apps you no longer use, or store photos in the cloud instead of on your phone. The images will stay on your phone in low quality to take up less storage but the full quality versions will stay in iCloud Photos.

Set up and use iCloud Photos - Apple Support

What is taking up the majority of your space? If you go to Settings > General > iPhone Storage it should lay out how all your data is being used.

If you have a bunch of storage for Photos, you can turn on iCloud Photos and choose a setting that leaves lower res photos on your device, but keeps a full res on in iCloud.

Set up and use iCloud Photos - Apple Support

When you view the breakdown, I have seen several comment that the 'other' category has gotten out of hand.. If it's taking up more than ~10 GB or so, try force restarting your phone

Force restart iPhone - Apple Support

If 'other' storage is still high, you may have to backup, reset and restore your phone

How to back up your iPhone, iPad, and iPod touch - Apple Support

Restore your iPhone, iPad, or iPod to factory settings - Apple Support

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

If the storage graph shows other stuff like large apps, or other misc files/data, you may have to go thru and find stuff to delete. Or upgrade to a phone with more storage capacity.

Cloud storage does not increase the amount of local storage on your phone.