Using older versions of Outlook for Mac for personal email and calendar
It turns out that this was related to something about the way the email was migrated from our previous email company to Microsoft, and the during the transition, both were operational. It only affected Apple Mail users. To make the sent messages go where they should (Sent Items), the previous vendor had to be completely removed from Apple Mail.
In all Apple Mail users, during the transition, sent messages were going to a subfolder of Exchange's inbox. In Big Sur Apple Mail, the sent-to names were showing in that list, as one would expect in a sent mail list. In Apple Mail versions before Big Sur, the sender's names were showing in the list, making the list of no practical value. At any rate, once the previous vendor email account was deleted from Apple Mail, Exchange started putting messages in Sent Items, where they belong, with the sent-to name showing in the list.