If you're looking for an alternate way to organize and find files on your Mac desktop, the issue with Lightroom Classic is that it is designed to only import image files, and mostly from cameras.
Adobe Bridge can browse, filter, and find a much wider range of file types because it has to work with many more Creative Cloud apps such as Adobe Illustrator (vector graphics), Adobe InDesign (page layout), video, and yes, PDF. Although Microsoft Word (.doc/.docx) files are not by Adobe, Bridge does see those too. And Adobe Bridge has Collections and Smart Collections like Lightroom Classic does. So maybe Adobe Bridge is an option, because it’s already included with your Creative Cloud subscription.
If you’re interested in organizing with something like Smart Collections, you don’t need any software for that, because the macOS Finder lets you create Smart Folders which are pretty much the same thing (a dynamic list based on search criteria).
There are also other Mac applications that let you browse, catalog, and organize a wide range of file types similarly to Lightroom Classic and Bridge, such as NeoFinder (paid software).