No text entry for iMessage recipients in Messages app

It turned out that both parties (myself and the other person) had already set our devices to send and receive from our phone numbers. However, it appears that years ago when we first started our conversation, we initiated it using iCloud email addresses. So since that time Messages had kept the conversation going on that basis.

We started a new conversation using our phone numbers, and that appears to have fixed the issue. Since the phone numbers and emails were already associated in our Contacts app, Messages imported all the old conversations into the new one automatically. This appears to have resolved the issue of the missing reply control bar and text entry field.

I found that I had other iMessage contacts after all. After a more thorough investigation, it seems this issue only affects contacts when their messages come from an email address (.mac, .icloud, etc.) instead of a phone number.

On an iPhone, users can go to Settings > Messages > Send and Receive > Start New Conversations From…, and choose a phone number or an iCloud email address. On a Mac, this can be configured in the Messages app under Preferences > iMessage pane > Start new conversations from.

I don't see a way to mark this as "Unsolved", because it turns out that the solution I found is only a temporary workaround. It reverts to the problem behavior each time the app is closed. So then I have to start a new conversation to the phone number each time to fix it.