Does Catalina device sync log what it's doing?
The heavy lifting seems to be handled by AMPDevicesAgent (AMP = Apple Media Player?). It logs some information to the system, which is available via Terminal with the log show and log stream commands.

This log show will show the past hour of activity.

    log show \
        --info \
        --last 1h \
        --signpost \
        --style compact \
        --predicate 'senderImagePath contains[cd] "AMPDevicesAgent"'


This log stream will show activity as it happens.

        log stream \
        --info \
        --signpost \
        --style compact \
        --predicate 'senderImagePath contains[cd] "AMPDevicesAgent"'


I like to wrap these up in bash functions, so autocomplete will see them.

function ampdevicesagent-log-show() {
    log show \
        --info \
        --last 1h \
        --signpost \
        --style compact \
        --predicate 'senderImagePath contains[cd] "AMPDevicesAgent"'
}

function ampdevicesagent-log-stream() {
    log stream \
        --info \
        --signpost \
        --style compact \
        --predicate 'senderImagePath contains[cd] "AMPDevicesAgent"'
}


The output is noisy and ugly, but includes some useful information. For example I can see dataclass Photo, so AMPDevicesAgent is working on my photos.

2019-11-08 10:01:21.112 I  AMPDevicesAgent[8032:4b63e] [com.apple.AMPDevicesAgent:device] airtraffic&gt; sending FileComplete for device id 24E310219F9516D1, asset identifier "04B3983D-75F1-4252-8CEC-FE87D05B1046", dataclass Photo (716), path "&lt;private&gt;"
2019-11-08 10:01:21.118 I  AMPDevicesAgent[8032:4b63e] [com.apple.AMPDevicesAgent:device] stats&gt; totalDiskBytes = 255989469184, freeDiskBytes = 74330591232 (reservedDiskBytes = 460324864)
2019-11-08 10:01:21.969 I  AMPDevicesAgent[8032:4b63e] [com.apple.AMPDevicesAgent:device] airtraffic&gt; sending FileComplete for device id 24E310219F9516D1, asset identifier "64FCE71F-0B7F-48C8-9F6F-E938D61C08EB", dataclass Photo (717), path "&lt;private&gt;"
2019-11-08 10:01:21.990 I  AMPDevicesAgent[8032:4b63e] [com.apple.AMPDevicesAgent:device] stats&gt; totalDiskBytes = 255989469184, freeDiskBytes = 74329260032 (reservedDiskBytes = 460324864)
2019-11-08 10:01:25.199 I  AMPDevicesAgent[8032:4b63e] [com.apple.AMPDevicesAgent:device] airtraffic&gt; sending FileComplete for device id 24E310219F9516D1, asset identifier "CD7C8B0A-85F1-4D16-8777-0F490976D366", dataclass Photo (718), path "&lt;private&gt;"


There's also some potentially useful information about totals:

2019-11-08 10:05:57.930 I  AMPDevicesAgent[8032:1b65c] [com.apple.AMPDevicesAgent:device] totals&gt; totalAudioTracks = 2000, totalAudioBytes = 19275661312 (17.95 GB)
2019-11-08 10:05:57.930 I  AMPDevicesAgent[8032:1b65c] [com.apple.AMPDevicesAgent:device] totals&gt; totalVideoTracks = 44, totalVideoBytes = 9366544384 (8.72 GB)
2019-11-08 10:05:57.930 I  AMPDevicesAgent[8032:1b65c] [com.apple.AMPDevicesAgent:device] totals&gt; totalGames = 0, totalGameBytes = 0 (0.00 GB)
2019-11-08 10:05:57.930 I  AMPDevicesAgent[8032:1b65c] [com.apple.AMPDevicesAgent:device] totals&gt; totalApplications = 49, totalApplicationBytes = 4917116928 (4.58 GB)
2019-11-08 10:05:57.930 I  AMPDevicesAgent[8032:1b65c] [com.apple.AMPDevicesAgent:device] totals&gt; totalPhotos = 656, totalPhotoBytes = 3300793216 (3.07 GB)
2019-11-08 10:05:57.930 I  AMPDevicesAgent[8032:1b65c] [com.apple.AMPDevicesAgent:device] totals&gt; otherDiskBytes = 0 (0.00 GB)


However totalPhotos = 656 doesn't seem to line up with dataclass Photo (718).