Messages are syncing fine on my iPad and my iPhone (both iOS 15.7.1) but are no longer arriving on my iMac (OS 10.14.6). I have checked all settings and everything appears to be correct. Somewhere else I could look?

No messages syncing on your iMac? I have observed that only messages that come from an iPhone will sync on my iMac.
Non-iPhone messages are received via cellular on an iPhone, and desktop Macs don't have cellular.

Both iMessage and SMS messages addressed using either a phone number or Apple ID associated with the same Apple account should appear on any Apple device logged onto that account. By the same token any device on that account with an internet connection can make or receive telephone calls. I make and receive phone calls and MMS messsages on my Mac every day. (The cacophony when a phone call is received and all three devices ring simultaneously can be nerve shattering). I am unaware of any setup other than logging all three devices onto the same Apple ID.

In view of my admitted ignorance on this topic I have two suggestions:

1. On your Mac: Go to System Settings > Apple ID and sign out then sign back in again being careful to use the same Apple ID and password you used on the iPhone and iPad. If that doesn't get your messages back in synch then...
2. Go here[ and chat with Apple Tech Support (no charge).

Thanks. Where do I find System Settings? I have the System Preferences window but it doesn't have an icon for Apple ID.

Edit: There is an iCloud icon. Should I use it?

Are you certain about SMS messages appearing on a desktop (no cellular service) Mac? I have yet to see them on any iMac or non-cellular iPad.

Absolutely positive! I just deleted half a hundred texts from different candidates wanting money.

A late reply to this post, but SMS messages, that is messages to a non-iPhone, only appear on a desktop Mac if Text Message Forwarding is turned On in the iPhone in Settings>Messages. If you have more than one Mac, in this setting you can select which Macs get the forwarded SMS messages.

I must be getting old I forget all about that switch on the iPhone. and when I checked I found these settings. But all of my iMessages are synchronized on my iPhone, iPad, Watch, and Mac Studio along with most, but in retrospect I realize perhaps not all SMS messages. Then it struck me, the odd device out is the iPad which may or may not have cellular capability. My iPad does have cellular capability and shares the same phone number as the iPhone. (My Apple watch has cellular capabiity as well and I can send and receive messages on it without any help of support from my iPhone, so why isn't the watch a Text Messaging Forwarding option on the iPhone?)

To make a short story longer, on the iPhone, I have now enabled Text Message Forwarding to both my Mac and iPad and I will be monitoring iMessage and SMS texts closely to see the results. i should have a report on my findings in a few days.

It has always been toggled on and it has an iMac (we have only one) so I assume it should work.