Outlook Sync/Cache Issue - Most Recent Emails Don't Show

When you search for them, can you identify in which folder they are?

See; Determine the folder path of a message found in Search results - Robert 365

Note that many search queries are performed against the online mailbox index and not the local one. Therefore, double-check against the contents of the mailbox via Outlook on the Web as well.

If the user is/was blocked it will show up in the Restricted Entities section of the Microsoft Defender portal.
That can be accessed here; https://security.microsoft.com/restrictedentities

However, shouldn't affect incoming emails for that user.