Syncing Apple mail between multiple computers

You need to use the iMap protocol.

see comcast's write up.

https://www.xfinity.com/support/articles/email-client-programs-with-xfinity-email

I do not know about iCloud mail. It looks the same as any other email. See:

https://support.apple.com/en-us/HT202304

Mail isn't integrated as you suspect.

R

I have two iMacs and a MacBook Pro signed in to the same Apple ID

not relevant. Your apple id doesn't enter into the "picture"

using the same email addresses (iCloud and Comcast addresses). On my new iMac

(Retina 5K, 27-inch, 2020) I have read all the email in my inboxes but I

don't see any evidence of that on my old iMac (Retina 5K, 27-inch, Late

2014).

These accounts are not configured with the imap protocol.

The computers are on the same wired and WiFi networks

... not relevant

—and I use iCloud.

so your writing about your comcast and iCloud email

My iPhone sees that the email has been read.

when you set up an email on your iPhone it uses the imap protocol. At one time, iPhone mail only supported imap.

I had hoped that the "Synchronize all accounts" choice under the Mailbox menu would do

something but it seems to have no effect.

See here [ & seems surprising that apple included the option because of their minimalist approach. ]

https://apple.stackexchange.com/questions/12324/what-does-synchronize-mean-in-mail-app

The laptop also does not sync.

... ditto

I try to maintain an inbox-zero where I archive or delete all of the

mail that comes to the inbox but I don't want to have to do that on each

computer.

Help. I have updated to the latest MacOS and iOS.

... not relevant.

R

Super.

R