I think the culprit that is adding confusion to the pot is the difference between iMessage and SMS/MMS texts. Please bear with me while I elaborate...
- [b]Do not confuse the iMessage system with the Message App although they are closely inter-linked.
- iMessage© is a proprietary messaging system between Apple IDs via the internet and offers several very useful advanced features such as acknowledgment of message receipt and message being read as well as synchronizing between devices on the same AppleID.
- SMS/MMS are simplistic telecommunications protocols designed for use on relatively dumb (non-internet) devices and is devoid of all but the most rudimentary handshaking and lacks the acknowledgment, and synchronization features in iMessage.
- The confusion arises because the Message app in macOS, iOS, and iPadOS handles iMessage and SMS/MMS traffic almost transparently. (Outgoing iMessage texts are in a blue bubble while SMS/MMS are in a green bubble).
- As far as I can determine, the synchronization feature of iMessage is a function of the iMessage system independent of iCloud. (ie. I have no idea how to shut it off or even if it can be shut off.)
- The iMessage protocol is similar to IMAP in email in that all the devices are "seeing" the same server content and what you do on one device effects all of the devices on the same account.
- SMS/MMS appears to work more on a "broadcast" basis. The message is broadcast over the telco network as a message with an attached address to be "picked up" by any device listening for texts with that address. As a result any given SMS/MMS text may be picked up by all of the devices, some of the devices, or none of the devices using that address. So what happens to an SMS/MMS on one device has no linkage to what happens to that same message on any other device, unless iCloud synchronization intervenes. (My Apple Watch drives me crazy because MMS messages pile up on it and I don't think of deleting them until there are a ton of messages waiting to be individually deleted that have already been deleted on my iPhone, iPad, and Mac. I would remove Message from the watch if it weren't so useful at times.)
With that in mind, the only solution I can think of is sending Feedback to Apple and maybe they can figure out changes to iMessage and/or Messsage to solve your/our problems.