So, as it turns out, no need to talk to my carrier about SMS/RCS message and message read state synchronization.
The sync problems I was having with iMessages (threads with blue bubbles) was fixed by resetting iMessages by turning iMessages off and on both my Mac and iPhone. After that, iMessages and message read state were synchronized.
For SMS/RCS messages (message threads with green vs blue bubbles) the culprit was the automatic deletion of verification codes. For instruction on turning that feature on and off, see the following URL way down at the bottom of the page:
Automatically fill in one-time verification codes on iPhone - Apple Support
I believe the trick is to make sure however you have this set, it needs to be consistent between devices. A mismatch causes the synchronization problem. The messages will be truly synchronized with the feature off. With the feature on, the verification message will only be deleted on the device that consumes the code. The code will still appear on the other devices but it's read state will be as having been read.
I have to admit, I'm a bit mystified why this is even an interesting feature. Once a verification code is used, it ceases to be valid for subsequent use. If it is unused, they typically time out in a matter of minutes so I'm at a bit of a loss to understand why Apple even bothers with this feature.
FWIW, I do *not* have Messages turned on in iCloud. I am using the text forwarding technique documented at:
Forward text messages from your iPhone to other devices - Apple Support