why are my messages not updating on my Mac

Both Test Message Forwarding and Messages in iCloud need to be enabled:

How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac - Apple Support

Use Messages in iCloud - Apple Support

If it worked in the past and just recently stopped working, the usual remedy is to use the Messages app's Preferences... > iMessage > Settings. Make sure both "Enable this account" and "Enable messages in iCloud" are selected. Select "Sync Now".

If your messages still don't carry over, click "Sign Out" and confirm the dialog that appears next. Then, "Sign In" again.

Set up iCloud on all your devices

Keep your messages up to date with iCloud

And on the iPhone Setting >> Messages and enable " Text Forwarding ".

Make sure in there( iPhone ) the Apple Computer is listed and enabled