As far as I know the slaves were non Muslim,
and if there accept Islam they cannot be kept as slaves
This is wrong. Slaves can be Muslims. There are verses in the Quran which mention Muslim (believing) slaves such as 4:25 and 4:92 and 2:221. The actual rule is that only a Harbi Kafir can be enslaved while a Free Muslim can never be enslaved. This says nothing about a disbeliever who is first enslaved and later accepts Islam.
It is possible for Muslim slaves to exist through the following means:
A Harbi disbeliever who has been captured and then accepts Islam can be enslaved.
A slave who converts to Islam remains a slave.
A child of a Muslim slave woman through marriage with other than its owner, is a slave.
The quote you have given from Adwa’ al-Bayaan of al-Shanqeeti says the same. You have only given a partial quote which is a question that Shanqeeti answers and you seem to have ignored the answer. Shanqeeti says the following:
If it is said: If the slave is a Muslim, how can he be kept as a
slave if the reason for which people may be taken as slaves is if they
are kaafirs who are waging war against Allaah and His Messenger?
answer is that the basic principle which is well known to the scholars
and all wise people is that a right that is already established by
shar’i means cannot be superceded by rights that are established later
When the Muslims take prisoners of war, they are given the right to
enslave them by the law of the Creator of all, and He is the All-Wise,
All-Aware. If this right is established, then the slave becomes a
Muslim after that, his right to be freed from slavery because of his
Islam is superceded by the right of the mujaahid whose right to
enslave him took effect before he was a Muslim. It is not just or fair
to waive the former right because of a latter right, as is well known
to all wise people
what should a master do if his slave woman wants to convert
He does not have to do anything as conversion to Islam of a concubine makes no difference. As noted above she remains a slave. And also sexual relations via concubinage remain permissible with her. Indeed, her being a Muslim, Jewess or Christian is actually requirement for concubinage according to the majority opinion.
أن تكون الجارية مسلمة أو كتابية إذا كان المتسري مسلما
For a Muslim master the concubine must be a Muslim or Kitabee
— Encyclopedia of Islamic Jurisprudence
قال: إني مسلم. فقال: لو قلتها وأنت تملك أمرك أفلحت كل الفلاح ... ففدي بالرجلين
(the prisoner said): I am (now) a Muslim. (The Prophet said): Had you said this when you had been the master of yourself, you would have gained every success ... he was then ransomed for two persons.
— Sahih Muslim - Sharah: إذا أسلمت بعد الأسر فيسقط الخيار في قتلك ويبقى الخيار بين الاسترقاق والمن والفداء
Note: This answer is with respect to a Muslim master. If a Dhimmi possesses a slave who is a Muslim then that slave must be sold to a Muslim owner. As disbelievers can not have authority over muslims under Islamic laws.