How to delete other users/acct iMessages on iPad after new log in?

I’m on an iPad Air with OS 16.6.1. I’ve logged out of my iCloud accounts with my ID so my wife can use the iPad with her acct/ID. When I’ve logged her out of iMessages I still can see all her last messages in the column tab and the last 4 contacts when I long press the iMessages app (Incl name, phone and email - used as a feature shortcut when logged in).

#1 this is a security/privacy issue that I can still view this info, even though the app has a pop up window asking me to log back into iCloud for iMessages.

#2, when I log into my account in iMessages, I still can see the entire list of her past message and when I click in, I can see all the past messages since she was last logged in. #2 BIG secure/privacy issue.

QUESTION: When I log out of these accounts (iCloud/iMessages specifically) how can I ensure all past messages and contact information is deleted/purged from the iPad so I can’t see this info (and she can’t see mine when I log out of my account and she logs back in)?

I don’t seem to have this issue with CONTACTS app or FaceTime app… just iMessages on the iPad.

Thanks