It’s behaving like you haven’t received new emails. You need to change folders. For Example: If somebody send an email to me and I start the Outlook, or it’s opened, I have to change between folders, ex: From Received, I have to change to sent emails, and back to received, and from then, I can see the emails. Then if somebody send me another, I have to change between folders to receive it again.

I tried to download the latest M365 version, everything is up to date.