In SharePoint Online, when you create a new managed property, it will have some limitations. For example, the property can only be of typeText or Yes/No, and it can’t be refinable or sortable.
Yup, no sorting for you, and no refinement panel goodness. And no search queries against date ranges. You can potentially search for a particular date, but not ‘between 1st Feb and 23rd March’.
I hope Microsoft can improve this function at least provide date ranges for the search query