Mail: Disappearing email in Mail

2019 27" iMac, Ventura 13.6, Mail Version 16.0 (3731.700.6), Safari Version 17.0 (18616.1.27.111.22, 18616)

As soon as I read an email in my inbox of Mail (MacOS), look at another folder and look back to the inbox, the read email is gone.

I look at the same inbox using my browser (Safari) logged into the same email account, the email is sitting there. If I use the browser to relabel the email as unread, it reappears in Mail in the inbox.

My email account is an account through the professional organization Institute of Electrical and Electronic Engineers (IEEE) and it is actually provided by Google. It is a flavor of gmail.

Is there some setting in Mail that I have overlooked which needs to be put right or am I suffering the joys of gmail? Is there a setting in the browser which needs fixing?