There is no way to visually browse or read individual text messages directly on the iCloud.com website, as Apple does not provide a web interface for the Messages app. While iCloud may still show that storage is being used after you have erased messages from your devices, this is often because "orphan" data or large attachments remain indexed on Apple's servers.
To see what remains, you can sign into a new or wiped device and enable Messages in iCloud to force a download of the cloud data, or you can manage the specific files by navigating to Settings > [Your Name] > iCloud > Manage Account Storage > Messages. If you wish to clear everything entirely, you can select "Disable & Delete" in your message storage settings to remove all data from the cloud after a 30-day grace period.