Spent some quality time with Apple support on this issue. There definitely is a difference in read state synchronization between iMessages and standard text messages which now use the RCS standard.
If a conversation is *all* iMessage participants, read status is synchronized via iMessage protocol. If it's not working for you, a debug step is to turn off iMessages on both your phone and your Mac and then turn it back on. I, for example, am using the "set up Text Message Forwarding separately" instructions and do not have Messages turned on in iCloud. After the debug step, my iMessage read statuses are synced.
Forward text messages from your iPhone to other devices - Apple Support
Standard RCS text message read state is controlled by your phone carrier. So if a conversation is *not* iMessage (the incoming bubbles are green not blue) and your read status is not synchronized, you need to have a conversation with your phone carrier. I've not done that yet because I ran out of time today. I'll follow up once I have that resolved.
The secondary problem I was having was that one time codes sent via RCS were not showing up in my Mac Messages client. I'd get a notification of the code coming in and the code would be available for autofill in Safari but the message with the code would not appear in the Messages client. That, as it turns out, was because of the feature to automatically delete one time codes. That feature can be found by going to System Settings > General > AutoFill & Passwords > Verification Codes. It is a simple toggle switch. Once I turned "Delete after use" off, the messages with the codes were once again appearing in my Mac client. Now, I don't know when this switch got thrown for me. All I can say is that *I* never changed it and the codes used to appear in my Mac Messages client so I don't know if the issue is that the default changed or that the behavior changed.
So that's all I know for now.