I noticed that when I search for something in a document library and click "See All" for all the search results, the filter icon in the top right corner disappears and I am unable to use any of the columns to filter the results. Is this the intended behavior, and is there no way to enable filtering of search results? Or are users only going to be able to filter before searching?
according to the official doc, there is no way to enable filtering of search results.
"The modern search experience doesn't support changing the sort order of results or building refiners based on metadata. Therefore, the following search schema settings don’t affect the modern search experience" Quote from here
And the MS staff is now working on adding this functionality
"Work is ongoing on adding new filters and custom filters. Don't have a ETA yet but we are experimenting with among others author refiners."
You can check this thread about information from engineers working on this part: https://techcommunity.microsoft.com/t5/SharePoint/SharePoint-Online-Search-Filters-Managed-Metadata/td-p/209259
You can customize SharePoint Online Search and Search results with PNP Modern Search WebParts in a fine granular manner: