My findings

AudibleTag.cs

    public class AudibleTag
    {
        public string LONG_DESCRIPTION { get; set; }

        /// <summary>
        /// eg: Transport: Transport 1
        /// </summary>
        public string SHORT_TITLE { get; set; }

        /// <summary>
        /// eg: B00W5I55F0
        /// </summary>
        public string ASIN { get; set; }

        /// <summary>
        /// eg: ADBL
        /// </summary>
        public string TYPE { get; set; }

        /// <summary>
        /// 110050
        /// </summary>
        public string VERSION { get; set; }

        /// <summary>
        /// A1TG7EBYOIJUO2
        /// </summary>
        public string GUID { get; set; }

        /// <summary>
        /// CR!2NN7KCDZB559X6V792C6DP0ZP67N
        /// </summary>
        public string AACR { get; set; }

        //BK_ADKO_002144
        public string ProductId { get; set; }
        public string Publisher { get; private set; }
        public string Narrator { get; set; }
        public string ReleaseDate { get; private set; }



        public string AUTHOR { get; set; }
        public string CATEGORY { get; set; }
        public string COPYRIGHT { get; set; }
        public string COVER_ART { get; set; }
        public string PARENT_PRODUCT_ID { get; set; }
        public string PARENT_TITLE { get; set; }
        public string PRODUCT_ID { get; set; }
        public string PROVIDER { get; set; }
        public string PUBLISH_DATE { get; set; }
        public string SHORT_DESCRIPTION { get; set; }
        public string SUBCATEGORY { get; set; }
        public string TITLE { get; set; }
        public string USER_ALIAS { get; set; }
        public string PARENT_SHORT_TITLE { get; set; }
        public string TRACK_NUMBER { get; set; }

        public string SynchronizedImage { get; set; }
        public string Png { get; set; }

        /// <summary>
        /// This one is a wild guess.
        /// In case of https://www.audible.de/pd/B01FMANLM6 (Dämonenblut / Nachtfeuer / Perlmond)
        /// Asin is B01FMANQU8 and Parent_Asin is B01FMANLM6
        /// Asin is not available via their official website, but the child is listed as such on their api (https://api.audible.de/1.0/catalog/products/B01FMANLM6?response_groups=contributors,media,price,product_attrs,product_desc,product_extended_attrs,product_plans,rating,review_attrs,sample,sku,series,relationships,badges)
        /// </summary>
        public string Parent_ASIN { get; private set; }

        public static AudibleTag FromTrack(Track track)
        {
            return new AudibleTag
            {
                LONG_DESCRIPTION = ValueOrEmpty(track.AdditionalFields, "@lde", "©des"), // lde was not there in my case
                SHORT_TITLE = ValueOrEmpty(track.AdditionalFields, "@sti"), // Transport: Transport 1
                ASIN = ValueOrEmpty(track.AdditionalFields, "CDEK"),     // B00W5I55F0
                Parent_ASIN = ValueOrEmpty(track.AdditionalFields, "PASN"), // Asin: B00W5I55F0
                TYPE = ValueOrEmpty(track.AdditionalFields, "CDET"),     // ADBL
                VERSION = ValueOrEmpty(track.AdditionalFields, "VERS"),  // 110050
                GUID = ValueOrEmpty(track.AdditionalFields, "GUID"),     //"A1TG7EBYOIJUO2"
                AACR = ValueOrEmpty(track.AdditionalFields, "AACR"),     //"CR!2NN7KCDZB559X6V792C6DP0ZP67N"
                ProductId = ValueOrEmpty(track.AdditionalFields, "prID"),    // BK_ADKO_002144
                Publisher = ValueOrEmpty(track.AdditionalFields, "©pub"),     // Audible Studios
                Narrator = ValueOrEmpty(track.AdditionalFields, "@nar", "©nrt"),     // Heiko Grauel
                ReleaseDate = ValueOrEmpty(track.AdditionalFields, "rldt"),  // 28-MAY-2015

                // Those came out empty in my tests ....
                AUTHOR = ValueOrEmpty(track.AdditionalFields, "@aut"),
                CATEGORY = ValueOrEmpty(track.AdditionalFields, "@cat"),
                COPYRIGHT = ValueOrEmpty(track.AdditionalFields, "@cop"),
                COVER_ART = ValueOrEmpty(track.AdditionalFields, "@car"),
                PARENT_PRODUCT_ID = ValueOrEmpty(track.AdditionalFields, "@ppi"),
                PARENT_TITLE = ValueOrEmpty(track.AdditionalFields, "@pti"),
                PRODUCT_ID = ValueOrEmpty(track.AdditionalFields, "@pid"),
                PROVIDER = ValueOrEmpty(track.AdditionalFields, "@pro"),
                PUBLISH_DATE = ValueOrEmpty(track.AdditionalFields, "@pda"),
                SHORT_DESCRIPTION = ValueOrEmpty(track.AdditionalFields, "@sde"),
                SUBCATEGORY = ValueOrEmpty(track.AdditionalFields, "@sub"),
                TITLE = ValueOrEmpty(track.AdditionalFields, "@tit"),
                USER_ALIAS = ValueOrEmpty(track.AdditionalFields, "@ual"),
                PARENT_SHORT_TITLE = ValueOrEmpty(track.AdditionalFields, "@pst"),
                TRACK_NUMBER = ValueOrEmpty(track.AdditionalFields, "@tnu"),

                SynchronizedImage = ValueOrEmpty(track.AdditionalFields, "asyi"),
                Png = ValueOrEmpty(track.AdditionalFields, "png"),
            };
        }

        public static void ToTrack(AudibleTag tag, Track track)
        {
            WriteIfNotEmpty(track, tag.LONG_DESCRIPTION, "@des");
            WriteIfNotEmpty(track, tag.SHORT_TITLE, "@sti");
            WriteIfNotEmpty(track, tag.ASIN, "CDEK");
            WriteIfNotEmpty(track, tag.Parent_ASIN, "PASN");
            WriteIfNotEmpty(track, tag.TYPE, "CDET");
            WriteIfNotEmpty(track, tag.VERSION, "VERS");
            WriteIfNotEmpty(track, tag.GUID, "GUID");
            WriteIfNotEmpty(track, tag.AACR, "AACR");
            WriteIfNotEmpty(track, tag.ProductId, "prID");
            WriteIfNotEmpty(track, tag.Publisher, "©pub");
            WriteIfNotEmpty(track, tag.Narrator, "©nrt");
            WriteIfNotEmpty(track, tag.ReleaseDate, "rldt");
            WriteIfNotEmpty(track, tag.AUTHOR, "@aut");
            WriteIfNotEmpty(track, tag.CATEGORY, "@cat");
            WriteIfNotEmpty(track, tag.COPYRIGHT, "@cop");
            WriteIfNotEmpty(track, tag.COVER_ART, "@car");
            WriteIfNotEmpty(track, tag.PARENT_PRODUCT_ID, "@ppi");
            WriteIfNotEmpty(track, tag.PARENT_TITLE, "@pti");
            WriteIfNotEmpty(track, tag.PRODUCT_ID, "@pid");
            WriteIfNotEmpty(track, tag.PROVIDER, "@pro");
            WriteIfNotEmpty(track, tag.PUBLISH_DATE, "@pda");
            WriteIfNotEmpty(track, tag.SHORT_DESCRIPTION, "@sde");
            WriteIfNotEmpty(track, tag.SUBCATEGORY, "@sub");
            WriteIfNotEmpty(track, tag.TITLE, "@tit");
            WriteIfNotEmpty(track, tag.USER_ALIAS, "@ual");
            WriteIfNotEmpty(track, tag.PARENT_SHORT_TITLE, "@pst");
            WriteIfNotEmpty(track, tag.TRACK_NUMBER, "@tnu");
            WriteIfNotEmpty(track, tag.SynchronizedImage, "asyi");
            WriteIfNotEmpty(track, tag.Png, "png");
        }

        private static void WriteIfNotEmpty(Track track, string value, string key)
        {
            if (!string.IsNullOrEmpty(value))
            {
                track.AdditionalFields[key] = value;
            }
        }

        private static string ValueOrEmpty(IDictionary<string, string> dictionary, params string[] keys)
        {
            foreach (var key in keys ?? Array.Empty<string>())
            {
                if (dictionary.TryGetValue(key, out var value))
                {
                    dictionary.Remove(key);
                    return value;
                }
            }

            return string.Empty;
        }
    }