What we can see about your managed iOS device? It’s minimal and quite vague.
Here’s a list of what we can see:

• Amount of storage used on the device
• Battery charge percentage
• Installed apps, version, and how much space the app uses on the device
• Installed operating system version
• If a device is signed into an Apple ID (but not the actual Apple ID)
• If a device has a passcode (but not the actual passcode)

If you’re in a classroom where an Instructor is using Apple Classroom, they would have the ability to view your screen while you were both in the same space, but you would also receive a blue indicator in the corner of your screen to notify you that your screen was being viewed. Here’s more info on that in case you’re interested: https://support.apple.com/guide/classroom/view-and-lock-screens-cla36eee3ee2/3.6/ipados/14.5

What type of control can we have over your managed iOS device?
Here’s a breakdown:

• We can enforce certain configuration items, such as requiring a passcode (data on a device with a passcode is automatically encrypted)
• We can deploy applications
• We can remote erase (provided the device has an active internet connection)
• We may be able to remote clear a passcode if you forget yours (requires the device have an active internet connection and verification of your identity, so someone else can’t request your passcode be cleared)
• We can set/clear Lost Mode (this requires the device have an active internet connection)

One note on Lost Mode. This is the only way we would be able to track a managed device’s location, and there’s no way for us to do it without the user’s knowledge. When a device is in Lost Mode, it cannot be used and will display a message indicating it’s in Lost Mode. When a device that has been in Lost Mode is cleared from that mode, the user is notified the device’s location was tracked and requires the person sign back into their Apple ID to ensure no one can use their Apple ID without permission. Here’s more info on Lost Mode if you’re interested: https://support.apple.com/en-us/HT201472

This list is non-exhaustive and changes can happen to it periodically. In case we missed something here, be sure to check with Apple for the most comprehensive information.

https://www.apple.com/privacy/
https://support.apple.com/en-us/HT202837