.... Clearly, going by feedback from multiple users, there is a bug in the last update (2306 build 16529.20154) that needs rectifying at a higher level, unless someone can do some wizardry in the meantime...
Affected users might find some helpful information in Michael Chesley Johnson's 05-Jul-2023 Keep Getting "Outlook closed while you had items open. Reopen items from last session?" Even Though It's Not True.
Diane Poremsky [ M365 MVP] (who manages the excellent Outlook and Exchange Solutions Center at https://www.slipstick.com/) has posted in that thread that the registry entry that controls the appearance of the “Outlook closed while you had items open. Reopen those items from your last session?” prompt should be located located at :
HKEY\_CURRENT\_USER\Software\Microsoft\Office\16.0\Outlook\Preferences
DWORD: ReopenWindowsOption
I can confirm that this ReopenWindowsOption registry entry is missing from my Windows registry ...

... and the current assumption is that the Version 2306 / Build 16529.20154 (rel. 26-Jun-2023) update incorrectly deleted that registry entry for many users with a perpetual version of MS Office 2016 / 2019 / 2021 C2R (Current Channel).
Affected users who have manually re-created that registry entry and/or set the value to 1 (Never reopen previous items) have confirmed they stop seeing this prompt. Other permitted values for this registry entry are 0 [Ask me if I want to reopen previous items (i.e, the default that displays the prompt)] and 2 (Always reopen previous items).
Dell Inspiron 5584 * 64-bit Win 10 Pro v22H2 build 19045.3086 * Firefox v115.0.1 * Microsoft Defender v4.18.23050.5-1.1.23050.3 * Malwarebytes Premium 4.5.32.271-1.0.2051 * Macrium Reflect Free v8.0.7279 * Microsoft Office 2019 Home and Business 2019 Version 2306 / Build 16529.20154 C2R