Hello, Hutch1960. Thank you for posting your question to the Apple Support Communities. We understand your situation and how your read messages are not automatically being updated on all of your devices. We’re happy to help you research this and find out about any possible solutions.
To get started on this, we would like to let you know that not all messages will sync instantly across your devices. It may take some time to see changes in your message history reflected on your Mac.
If you notice that your read messages are never updated on your Mac, we can help you more with this. To continue, we would first suggest that you back up and update both devices. The following Apple Support articles explain which steps to follow when updating your devices:
Update your iPhone, iPad, or iPod touch - Apple Support
Update macOS on Mac - Apple Support
If you are not noticing an improvement after updating, we may suggest enabling iCloud for Messages on all of your devices. If you do not already have this feature enabled, you will need to use the same Apple ID with all of your devices. When this feature is enabled, iCloud should automatically keep your message history updated and available on your devices. The following two articles explain more about Message in iCloud:
Use Messages in iCloud - Apple Support
Set up iCloud for Messages on all your devices - Apple Support
We hope that these suggestions allow you to start seeing your message history updated as you would expect on your devices. You can reply back here if you have additional questions about these features.
Cheers!