iPad storage full and iCloud has lots of space

iCloud storage and iPad storage are completely different. Having more iCloud storage does NOT increase the physical memory on your iPad and iCloud is a syncing service not an archive.

The only thing you can do is delete things off the iPad you don't need or use, such as photos, videos, applications, text messages, email, etc.

Here's the problem. iCloud is not an Archive, so if you save photos in the cloud and then delete them from your iPad, they will delete from the cloud. To ensure you don't lose your photos, one of the simplest things do to would be connect your iPad to your home computer and upload your photos to your computer photo directory.

Here's a link which will help you --> Transfer photos and videos from your iPhone, iPad, or iPod touch - Apple Support

I would have recommended an app photo service like Google Photo or Amazon photo if you're a prime customer, but with so little space on your iPad, you would not be able to download an app to your device.

Ps: Apple no longer sells ANY device with only 16GB of memory for this very reason. In the near future it would be really good to consider a newer iPad with more memory. As you're learning, once purchased, there is NO WAY to add more memory to any iOS based device.

If you need to free up free data storage space on an iPad/iDevice, you need to start by backing up your iPad to either Apple's iCloud ( you may need to pay for additional, monthly storage space ) or by connecting your iDevice to a computer running the latest iTunes and/or some other offsite, “cloud” data storage/backup services, like Google Drive/Photos, DropBox, BOX, Amazon Cloud Drive, Flickr ( for photos/images ), etc.

Then, delete any installed apps that you no longer use or use infrequently enough that they aren't missed (you can always reinstalled any purchased or free apps at some time later, as you need them).

A disclaimer to the immediate advice above, if you own a 8 or 9-year old iPad, you SHOULD ONLY delete apps that you have ever seldom used or no longer use as there is NO WAY now, in 2020, to retrieve these old apps from the iOS App Store, any longer.

( Third party iOS app developers have permanently removed all of their older, legacy apps from Apple's iOS App Store servers forever!

There are NO more older, common and popular third party apps for old 8 and 9-year old iOS devices, any longer! )

Then, thin out/delete any music/videos/movies/TV shows/podcasts/screen recordings/images/eBooks/

eMagazine/iBooks/audio books/Documents/PDFs, etc.

If you use a POP email account on your iPad, delete/thin out any old saved emails that maybe saved to your iPad.

To permanently delete photos/images off of your iDevice go into the Photos app and find the Recently Deleted folder/album and permanently delete any photos/images stored in that folder/album.

Also, you can check to see what other stuff is eating up all your valuable data storage space by going into the Settings App,,General Settings Panel, in the right hand column, tap Storage & iCloud usage panel ( in iOS 11, it’s iPad Storage ), in the top Storage Panel, tap the Manage Storage panel, wait for a list of apps to generate that will tell you how much space each app is taking up on your iDevice.

Then, for older iPads or iPads with a Lightning connector, do a hard reset of your iPad by holding down both the Home and sleep/wake buttons simultaneously until your iPad goes to black and restarts with Apple logo, then release the buttons.

OR

The new hard reset procedure for newer iPad Pro models

Try the new hard reset procedure for the new 2018/2020 iPad Pro models.

1. Press and Release the Volume Up button.

2. Then immediately Press and Release the Volume Down button.

3. Then, Press and Hold the Power Button at the top. You will see the Slide to Power off button, but keep on holding down the Power Button until you see the Apple logo, then let it go.

Once you have performed all the steps, wait for a few seconds and your 2018 iPad Pro will boot up completely to the iPad Pro’s Lock screen.

iOS devices and iOS/iPadOS need to maintain, at the very least, a minimum of between 2-4 GBs of free data storage space, AT ALL TIMES, to insure normal/nominal functionalities/operation and general overall performance of any iOS device running iOS/iPadOS.

If not all of this solves your iPad storage issues, you may need to do a complete backup, erase and restore of your iPad model.

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

How to erase your iPhone, iPad, or 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

Good Luck to You!

A 16 GBs iOS is NOT too useful in 2020.

The amount of available, practical, usable storage is based not only on how much iOS/iPadOS takes up but on the actual size that 1.0 GB is equivalent to, which for Apple 1.0 GB ≈1.075 GBs

Also, iOS/iPadOS devices need to maintain a minimum constant of between 2-4 GBs to ensure nominal, expected performance and function of iOS/iPadOS.

Also, my “current” installation of iPadOS 13.2.3 takes up approx. 5.5 GBs of my iPad's internal storage space.

Then amount of internal data storage space your version of iPadOS may be greater than this!

So,

A 16 GBs storage iPad starts out, after initial drive formatting, at approx. 14.5 GBs of free, internal storage.

After the installation of iPadOS, at nearly 5.5 GBs, leaves 9 GBs of of free, internal data storage space.

iOS/iPadOS needs a minimum of 2-4 GBs of constant remaining storage, AT ALL TIMES to insure/ensure nominal, acceptable operation of all iOS/iPadOS functionalities.

This leaves a 16 GBs iPad with ONLY a practical, usable storage space of between 5 and 7 GBs AND THAT IS IT!

This is virtually NO internal data storage to do much of anything with that iPad!

This is why Apple quietly, silently did away with all 16 GBs iOS device back sometime in 2016.

Compare this to a 32 GBs storage iPad which starts out with approx 30 GBs, after drive formatting.

Minus 5.5 GBs for iOS leaves 24.5 GBs.Minus 2-4 GBs for iOS iPadOS system reserve equals approx. between 20.5- 22.5 GBs of usable data storage space.

That is over 3-3-1/2 times the practical, usable internal storage space of 16 GBs iPad!

The usable, practical, free internal data storage space goes upward even more with higher amounts of iOS device internal storage space sizes!

You're welcome and good luck.