Hi Patrick,
According to my research, currently, there is no such a built-in option in Outlook to archive items in searching results.
If you have more concerns on this feature, it is encouraged to visit the Outlook user voice forum:
https://outlook.uservoice.com/ to vote for a similar idea or post your own.
It is a place for customers to provide feedback about Outlook. What’s more, if an idea is high voted there by other customers, it is promising that Microsoft Product Team will take it
into consideration when designing the next version in the future.
Thank you for your understanding and support!
Regards,
Perry
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