I am an independent advisor investigating your inquiry.
Currently, the Search Folder functionality that stores reusable search results like unread messages in a designated folder is not available for OWA or mobile.
Several users have added this suggestion to the Microsoft feedback portal. I will post the link so you can add your request or vote on others.
Advanced Search Folders as Favorites (i.e., All Unread & Flagged) · Community (microsoft.com)
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