Apparently, I have two strikes against me. 1) I still connect my various iPhones and iPods to my Mac using a USB cable and 2) I own my own music, which means I have no reason ever to connect to the iCloud. I'm still operating by Apple's original strategy to use the Mac as the mother ship to connect to various devices. But this is increasingly difficult. I
As you say, Apple's changes to iTunes (now Music) make it more challenging—if not impossible—to "manually manage" content. There is still a "manually manage" option, but I don't think it does anything. Please correct me if I'm wrong.
After much trial and error, I settled on the following solution. Select "Sync Music to UserName's iPhone" with the "Selected Artists, Albums, Genres, Playlists" option. This of course erases all content on the device. You then can go into the Music app on the Mac and copy your music to the device. You can also create playlists and sync them. This is not a bad approach, per se, though not intuitive. This approach requires you to use Music and the Finder, whereas before you could manage content on your device using iTunes alone. Also, as far as I can tell, you can never "see" playlists on your iPhone or iPod through the Mac.
It's a strange new world and I'm just a dinosaur. I still think the iPod was one of Apple's most amazing inventions ever. I still own a classic iPod and an iPod Shuffle. But most people don't use iPods any more. They stream content from their iPhones.