What is the ruling on vowing not to eat a certain type of meat from a slaughtered animal with the intention of healing, if some of it was eaten after 10 years of recovery? And is this vow permissible in the first place?

Your vow is considered a vow to abandon something permissible, which is not binding and entails nothing according to the majority of scholars, because it is not a vow of an act of worship. The Prophet, peace and blessings be upon him, said: "A vow is only that by which the Face of Allah is sought." Some scholars are of the opinion that the person who makes a vow to abandon something permissible has the choice between fulfilling it or atoning for it with an expiation for an oath. Therefore, offering an expiation for an oath is more cautious.