The hadith appears in about the same wording in sahih al-Bukhari in the book wills and testaments and the book of military expeditions and in sunan an-Nasa'i and in al-Hakim's al-Mustadrak. Similar narrations not quoting the statement about slaves can be found in almost all known sunni hadith collections such as sahih Muslim, musnad Ahmad etc. on the authority of 'Aisha and other companions.
In fath al-Bary, ibn Hajar didn't waste much time explaining the matter of slave and slave-girls and just said:
وله : ( ولا عبدا ولا أمة ) أي في الرق ، وفيه دلالة على أن من ذكر من رقيق النبي - صلى الله عليه وسلم - في جميع الأخبار كان إما مات وإما أعتقه ، واستدل به على عتق أم الولد بناء على أن مارية والدة إبراهيم ابن النبي - صلى الله عليه وسلم - عاشت بعد النبي - صلى الله عليه وسلم - ، وأما على قول من قال إنها ماتت في حياته - صلى الله عليه وسلم - فلا حجة فيه . (source commentary on the hadith in the book of wills and testaments)
(My own translation take it with the necessary care!)
On the statement (nor slave nor slavegirl ولا عبدا ولا أمة): This is a link that all the slaves of the Prophet (peace and Allahs blessing be upon him) which were quoted in the news (akhbar)/Narrations have either been freed or death at the time of his (the Prophet's) death.
Also this was used an evidence for freeing the mother of a child, based on the fact (or assumption for the doubters of this statement) that Maria al-Qibtiya (Marie the Coptic) the mother of Ibrahim the son of the Prophet (peace and Allahs blessing be upon him) lived after the Prophet's death. While the statement that shed died during his lifetime has no evidence.
So it seems that they either died or were freed at the time of the Prophet's () death. Note that AFAIK most (if not all) of the slaves Muhammad() owned were gifts of other people among them his wives beside prisoners of war!
However in 'Omdat al-Qari عمدة القاري of the hanafi scholar Badr al-Din al-Ayni بدر الدين العيني the author said that in his history (at-tarikh) he had counted around 60 of slaves Muhammad possessed (among?) beside them around 20 slave-girls!
قَوْله: ( وَلَا عبدا وَلَا أمة) ، أَي: فِي الرّقية، لِأَنَّهُ كَانَ لَهُ عبيد وإماء، وَقد ذكرنَا فِي ( تاريخنا الْكَبِير) : أَنه كَانَ لَهُ عبيد مَا ينيف على سِتِّينَ، وَكَانَت لَهُ عشرُون أمة، فَهَذَا يدل على أَن مِنْهُم من مَاتَ فِي حَيَاة النَّبِي صلى الله عَلَيْهِ وَسلم، وَمِنْهُم من أعتقهم وَلم يبْق بعده عبد وَلَا أمة، وَهُوَ فِي الرّقية. (Source)
he also confirmed the statement of ibn Hajar that all either died before or were freed later.