No this is the whole point: if you are using iCloud backups, your messages are not backed up.
The _only_ online way to maintain your iMessages is (checks settings) "Messages in the Cloud", which is e2e encrypted - if you lose all your devices there is no recovery path except for the "iCloud Key Vault", but I honestly don't know if that can get you to a point where old messages can be recovered.
Please read this article. The Messages in iCloud sync feature is e2e encrypted - but the sync key itself for the e2e is included in the (non-e2e) iCloud Backup which is done every night.
From Apple themselves:
> For Messages in iCloud, if you have iCloud Backup turned on, your backup includes a copy of the key protecting your messages. This ensures you can recover your messages if you lose access to your Keychain and your trusted devices. When you turn off iCloud Backup, a new key is generated on your device to protect future messages and isn't stored by Apple.
This is actually worse. It means that Apple has the cross-device Messages in iCloud sync key in effectively unencrypted form from the backup the night before - which means that they can decrypt the iMessages as they sync between your devices in realtime. This enables realtime iMessage surveillance because of this backdoor in the end to end crypto (the effectively unencrypted iCloud Backup, which includes the e2e keys for the Messages in iCloud feature).
The technical term for this is "key escrow". When you escrow the key to the middle transit service that is supposedly end to end, you backdoor the end to end encryption.
The _only_ online way to maintain your iMessages is (checks settings) "Messages in the Cloud", which is e2e encrypted - if you lose all your devices there is no recovery path except for the "iCloud Key Vault", but I honestly don't know if that can get you to a point where old messages can be recovered.