As described, your Messages were configured to synchronise with iCloud. One of two scenarios has occurred...
1) You have fully signed-out from your personal AppleID account:
Settings > [Your Name / AppleID] > Sign Out
When signing out, you were presented with the option "keep a local copy" of your iCloud data during the sign-out process. When you subsequently signed-in to iCloud using your business AppleID account, the locally stored iCloud data from your personal AppleID was merged with your Business AppleID account.
2) You actually signed-out from iMessage:
Settings > Messages > Send & Receive > AppleID >[iMessage Account] Sign Out
Although you have signed-out from iMessage, you remain signed-in to iCloud with your personal AppleID.
Given your description - and the relative increased complexity of just signing-out from iMessage - I suspect that the first scenario applies. If so, your personal AppleID data, including your personal messages, have been merged with your business AppleID.
Having merged your AppleID account data, there is no simple method to undo the merge - other than to manually delete the personal data from your merged data.
Also be aware that if you have indeed signed-in to your business AppleID, you'll not be able to again change your signed-in AppleID account for 90-days.