Is it possible to have multiple users on an iPad? Like log out of iCloud, then log back in as a different iCloud account?

No.

Outside of schools that are part of an Apple Education program (which usually also requires enrollment, provisioning, and related network infrastructure), these are single-user devices.

The Mac is the multi-user device.

Family Sharing shares apps, media, and purchases, as well as some other features. Nothing relevant here.

In general, iPhones and iPads are one-user devices and not designed to provide a different user experience by signing in/out of iCloud etc. So any settings you change to 'limit' a user will apply to anyone that uses the iPad.

In order to avoid merging each users data, you’d need to sign out of iCloud, erase the device by restoring it as new in iTunes or using erase all content under settings. Then the next user could set it up and sign in to iCloud without merging the previous users data with their iCloud data.

This is effectively what the education deployment system does via a remote management server every time a different student gets a device from the school.

So, no, iOS does not support multiple users.