How do I stop Apple Music from duplicating songs when syncing

From If songs are missing from your music library after you turn on Sync Library - Apple Support:

Did you check the cloud status of songs on your Mac or PC?

1. Open the Apple Music app or iTunes for Windows.
2. In the sidebar, select Songs.
3. Show Cloud Status and Cloud Download.

• In the Apple Music app on Mac or iTunes for Windows: in the menu bar, choose View > Show View Options.
• In the Apple Music app for Windows: right-click on the headings bar.

4. Select Cloud Status and Cloud Download.

Look for the following statuses next to your songs to find out what to do.

An exclamation mark

The song can't be played or synced across your devices until the original file has been located.

1. Click the exclamation mark  next to the song.
2. A message will appear and ask if you’d like to locate the song. Click Locate.
3. If the song has been located, you'll be asked to use the location to find other missing songs in your library. If you see this message, click Find Files.

Waiting

The song won’t appear on your other devices because it’s waiting to sync.

1. Make sure that your computer is connected to the Internet.
2. Update Cloud Library.

• In the Apple Music app for Mac or iTunes for Windows, choose File > Library > Update Cloud Library. 
• In the Apple Music app for Windows, click Sidebar Actions . Then click Library > Update Cloud Library.

3. Wait for the song to sync. Then, check if the song appears on your other devices.

Removed

The song was deleted from another device that has Sync Library turned on.

If you want the song to appear on your other devices:

1. Make sure all of your devices are connected to the internet.
2. Click the arrow  next to the song.
3. Click Add to Cloud Music Library.
4. Update Cloud Library.

• In the Apple Music app for Mac or iTunes for Windows, choose File > Library > Update Cloud Library. 
• In the Apple Music app for Windows, click Sidebar Actions . Then choose Library > Update Cloud Library.

When you have both a local copy and cloud copy of the same track in the library, Apple Music should be able to resolve them down to a single reference. Signing out and in again typically fixes it, but if not it might be cause the local copy is being excluded for some reason, adding it to the library may merge it with the cloud reference. An alternate approach, albeit time consuming, would be to redownload the purchases, but you want to avoid that if possible.

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See Duplicate songs in iTunes/Music - Apple Community. It may help to sign out of your Apple ID, then sign back in.

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Try Add to iCloud and see what happens. Try with a single album first. Music should resolve things so that there is only one locally stored reference left in the library, which would be a cloud reference if you created a new empty library. Assuming that works repeat in bulk.

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What is the iCloud status of the locally downloaded tracks? Can you add to library and have them merge with the cloud copies? Test on a single album to start with.

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