cloud backup for messages?

No. Backups are there for disaster recovery. They are not long term storage. When you back up your phone, whether to iTunes or iCloud, previous backups are overwritten/deleted.

Delete a message or conversation

When you delete a message or conversation, you can't get it back. So make sure that you save important information from your messages.

To delete a message:

1. In a message conversation, touch and hold the message bubble that you want to delete, then tap More.
2. Tap , then tap Delete Message. If you want to delete all messages in the thread, tap Delete All in the upper-left corner. Then tap Delete Conversation.

To delete a single conversation, swipe left over the conversation that you want to delete, tap Delete, then tap Delete again to confirm. To delete more than one conversation, open Messages and tap Edit in the upper-left corner. Then tap the circle next to the conversations and tap Delete in the bottom-right corner.

To keep your messages for a certain amount of time, go to Settings > Messages > Keep Messages. Then select how long you want to keep your messages.

Use Messages on your iPhone, iPad, or iPod touch - Apple Support

https://support.apple.com/en-us/HT201287

You may get better and prompt responses if you may kindly provide the iPhone Model that you have and the iOS version if it is known to you.