My messages are not on icloud

You use the Messages application, which serves as an interface between your computer and iCloud.

Your MacBook should have a "Messages" application in your Applications Folder.

"On your Mac

1. Open Messages.
2. In the menu bar, choose Messages > Preferences.
3. Click iMessage.
4. Select the checkbox next to Enable Messages in iCloud."

See this article https://support.apple.com/en-in/HT208532

And as per this article https://support.apple.com/en-in/guide/icloud/mm0de0d4528d/1.0/icloud/1.0

Note: Although your messages are stored in iCloud, you cannot see them on iCloud.com.

Where are you looking for your messages?

These two Support Articles explain iCloud Messages:

1. Keep all your messages in iCloud - Apple Support
2. Get help with Messages in iCloud - Apple Support

You are welcome.