Messages in iCloud disappeared from iPhone

You access everything that's stored simply by opening messages on your phone. There isn't anything else besides that in the cloud. iCloud doesn't back up your messages, it just keeps them in sync. If you don't sync between devices it's probably not necessary to use messages in the cloud.

Messages in the cloud simply synchronizes your messages across your devices. It is not a backup for your messages. If messages have been deleted from your phone, they are gone. you could restore from a backup made to your computer but that is at the expense of anything new since the last backup.