Same issue happened to me. You added the local files to your playlist, the playlist shows up on your phone and you try to download the songs, it says Downloaded, but they didn't actually download and are greyed out. These are the steps that should solve your issue since it worked for me. Both devices must be connected to the same Wi-fi network or else this won't work.
What you should do is first make sure both your phone and PC are connected to the same Wi-fi network. This won't work if your computer only has Ethernet capabilities, so you may need to look into getting a Wi-fi adapter for that. Then log out of Spotify on your phone, log back in, and try downloading again. They should download this time. On Android, go to Settings and toggle off "Download using cellular" because you're gonna be downloading using Wi-fi. For iOS users, go to Settings > Local files > Switch on Local audio files. If that doesn't work, switch to cellular instead because sometimes Spotify won't download songs if you have an unreliable internet connection. That, or switch back to Wi-fi and try again. Also make sure that Spotify on your phone and PC are both up to date. You could also try maybe deleting the songs in the playlist or the playlist itself, send the folder to the Recycle Bin, restore it, try adding the songs again, and try downloading again. Make sure you have the right folder in the local files enabled.
If that doesn't work, try looking to see if Spotify is being blocked by Windows Defender or a vendor firewall (i.e. Mcafee, Norton, ect.). If it is, try giving it access private and public.
Maybe this is some sort of bug in the Spotify app and I'm hoping it gets fixed in a future update. That, or Spotify needs to recalibrate/sync the local files again.