It seems to be getting worse. When I open my Outlook 2021 retail version now 3 inboxes and two messages that were previously closed open up again....
Hi garrybock (and other affected users):
Have you received the Version 2307 / Build 16626.20132 update (released 26-Jul-2023), and if so is your MS Office 2021 behaving any differently since it was installed? If you haven't received this Version 2307 update yet and don't want to wait for it to be automatically installed you can go to File | Office Account | Updates Options and choose "Update Now". Note that the Current Channel release notes <here> indicate an even newer update Version 2307 / Build 16626.20134 (rel. 27-Jul-2023) was released late today that has a minor bug fix for display fonts so you might receive that newer build instead.
I manually updated to Version 2307 / Build 16626.20132 today and since then I haven't seen any “Outlook closed while you had items open. Reopen those items from your last session?” prompts at Outlook startup, but I've only been testing for a few hours and those prompts might eventually return. I'll post back if I see that prompt reappear again.
Unfortunately, the Version 2307 / Build 16626.20132 build did not fix my problem where the settings under the Start Up Options header at settings at File | Options | General | Start Up Options are missing ...

... and when I checked my registry I can see that the registry value ReopenWindowsOption at HKEY_CURRENT_USER\Software\Microsoft\Office\16.0\Outlook\Preferences is still missing as well.

Dell Inspiron 5584 * 64-bit Win 10 Pro v22H2 build 19045.3208 * Firefox v115.0.3 * Microsoft Defender v4.18.23050.9-1.1.23060.1005 * Malwarebytes Premium v4.5.33.272-1.0.2069 * Macrium Reflect Free v8.0.7279 * Microsoft Office 2019 Home and Business 2019 Version 2307 / Build 16626.20132 Click-to-Run