Embrace's code for handling drops from Catalina's Music app, due to Apple not following the API contract for file promises. You will need to register for the kPasteboardTypeFileURLPromise drag type.

gistfile1.m

- (NSArray<NSURL *> *) parsePasteboard:(NSPasteboard *)pasteboard
{
    NSMutableDictionary *trackIDToMetadataMap = [NSMutableDictionary dictionary];
    NSMutableArray *orderedTrackIDs  = [NSMutableArray array];

    NSMutableArray *metadataFileURLs = [NSMutableArray array];
    NSMutableArray *otherFileURLs    = [NSMutableArray array];
    
    auto parsePlaylist = ^(NSDictionary *playlist) {
        if (![playlist isKindOfClass:[NSDictionary class]]) {
            return;
        }

        NSArray *items = [playlist objectForKey:@"Playlist Items"];
        if (![items isKindOfClass:[NSArray class]]) {
            return;
        }
        
        for (NSDictionary *item in items) {
            if (![item isKindOfClass:[NSDictionary class]]) {
                continue;
            }
        
            id trackIDObject = [item objectForKey:@"Track ID"];
            if (![trackIDObject respondsToSelector:@selector(integerValue)]) {
                trackIDObject = nil;
            }

            NSInteger trackID = [trackIDObject integerValue];
            if (trackID) [orderedTrackIDs addObject:@(trackID)];
        }
    };

    auto parsePlaylists = ^(NSArray *playlists) {
        if (![playlists isKindOfClass:[NSArray class]]) {
            return;
        }
        
        for (NSDictionary *playlist in playlists) {
            parsePlaylist(playlist);
        }
    };

    auto parseTrack = ^(NSString *key, NSDictionary *track) {
        if (![key isKindOfClass:[NSString class]]) {
            return;
        }

        if (![track isKindOfClass:[NSDictionary class]]) {
            return;
        }

        NSString *artist = [track objectForKey:@"Artist"];
        if (![artist isKindOfClass:[NSString class]]) artist = nil;

        NSString *name = [track objectForKey:@"Name"];
        if (![name isKindOfClass:[NSString class]]) name = nil;

        NSString *location = [track objectForKey:@"Location"];
        if (![location isKindOfClass:[NSString class]]) location = nil;
        
        if ([location hasPrefix:@"file:"]) {
            location = [[NSURL URLWithString:location] path];
        }

        id totalTimeObject = [track objectForKey:@"Total Time"];
        if (![totalTimeObject respondsToSelector:@selector(doubleValue)]) {
            totalTimeObject = nil;
        }

        id trackIDObject = [track objectForKey:@"Track ID"];
        if (![trackIDObject respondsToSelector:@selector(integerValue)]) {
            trackIDObject = nil;
        }
        
        NSTimeInterval totalTime = [totalTimeObject doubleValue] / 1000.0;
        NSInteger trackID   = [trackIDObject integerValue];
        
        if (!trackID) return;

        MusicAppPasteboardMetadata *metadata = [[MusicAppPasteboardMetadata alloc] init];
        [metadata setDuration:totalTime];
        [metadata setTitle:name];
        [metadata setArtist:artist];
        [metadata setLocation:sGetExpandedPath(location)];
        [metadata setTrackID:trackID];
        [metadata setDatabaseID:[key integerValue]];
        
        [trackIDToMetadataMap setObject:metadata forKey:@(trackID)];
    };

    auto parseTracks = ^(NSDictionary *tracks) {
        if (![tracks isKindOfClass:[NSDictionary class]]) {
            return;
        }
        
        for (NSString *key in tracks) {
            NSDictionary *track = [tracks objectForKey:key];
            parseTrack(key, track);
        }
    };

    auto parseMetadataRoot = ^(NSDictionary *root) {
        if (![root isKindOfClass:[NSDictionary class]]) {
            return;
        }

        parsePlaylists( [root objectForKey:@"Playlists"] );
        parseTracks(    [root objectForKey:@"Tracks"]    );
    };
    
    auto parsePasteboardItem = ^(NSPasteboardItem *item) {
        for (NSString *type in [item types]) {
            if ([type hasPrefix:@"com.apple."] && [type hasSuffix:@".metadata"]) {
                parseMetadataRoot([item propertyListForType:type]);
            }
        }
    };

    // Step 1, Fill metadataFileURLs from com.apple.*.metadata 
    {
        for (NSPasteboardItem *item in [pasteboard pasteboardItems]) {
            parsePasteboardItem(item);
        }

        for (NSNumber *trackID in orderedTrackIDs) {
            MusicAppPasteboardMetadata *metadata = [trackIDToMetadataMap objectForKey:trackID];
            
            NSString *location = [metadata location];
            NSURL    *fileURL  = location ? [NSURL fileURLWithPath:location] : nil;

            if (fileURL) [metadataFileURLs addObject:fileURL];
        }
    }

    // Step 2, Fill otherFileURLs with NSPasteboardTypeFileURL/kPasteboardTypeFileURLPromise
    {
        for (NSPasteboardItem *item in [pasteboard pasteboardItems]) {
            NSArray *types = [item types];

            BOOL hasPromise        = [types containsObject:(id)kPasteboardTypeFileURLPromise];
            BOOL hasPromiseContent = [types containsObject:(id)kPasteboardTypeFilePromiseContent];
              
            NSString *fileURLString = [item propertyListForType:NSPasteboardTypeFileURL];

            // In macOS Catalina 10.15.0, the new Music app likes to write a real URL
            // as a kPasteboardTypeFileURLPromise without kPasteboardTypeFilePromiseContent
            //
            if (!fileURLString && hasPromise && !hasPromiseContent) {
                fileURLString = [item propertyListForType:NSPasteboardTypeFileURL];
            }

            NSURL *fileURL = fileURLString ? [NSURL URLWithString:fileURLString] : nil;
            
            fileURL = [fileURL URLByStandardizingPath];
            fileURL = [fileURL URLByResolvingSymlinksInPath];
            
            if (fileURL) [otherFileURLs addObject:fileURL];
        }
    }

    // Step 3, Fill otherFileURLs with legacy NSFilenamesPboardType
    if ([otherFileURLs count] == 0) {
        NSArray *filenames = [pasteboard propertyListForType:NSFilenamesPboardType];

        if (filenames) {
            for (NSString *filename in filenames) {
                NSURL *url = [NSURL fileURLWithPath:sGetExpandedPath(filename)];
                if (url) [otherFileURLs addObject:url];
            }
        }
    }
    
    NSArray *fileURLs = [metadataFileURLs count] > [otherFileURLs count] ? metadataFileURLs : otherFileURLs;

    return fileURLs;
}