Removing shared albums from iPad without deleting from my iPhone

Shared Albums don't count against your iCloud Storage, but there are limits to the number of photos, albums, and invites that you can share.

You can learn more about the shared album here : Shared Album limits - Apple Support

If your iPad doesn't have enough storage check the Settings > General > [Device] Storage to see how we can free up space : How to check the storage on your iPhone and iPad - Apple Support

Because it was shared that is why it also update the changes made to other device.

When you check your iPad storage does it show Photos the one taking much of your storage ?

Great! Can you check if you have iCloud Photos enable on your iPad ?

To check go to Settings > Your name > iCloud > Show all apps > Photos