Click with right button mouse on Inbox >> Properties >> Repair Folder

Go to AppMenu button - Help - Troubleshooting Information - Profile Directory - Open Directory

This will open your profile folder in Windows Explorer (assuming you're using Windows).

Find your mail folder, either under 'Mail' or 'ImapMail', depending on your account type.

There should be a file Sent (w/o) a file extension. This file is supposed to contain your messages. What is the size of the file?

When you open the file with a text editor, do you see the missing messages?

I have an Apple Mac and am not using Windows. The "Sent" icon on the left side when I am using Thunderbird is empty, even though I have sent emails.

Then I guess it will open your profile folder in Finder or whatever the Mac file manager is called.