R Steinsaltz notes in his explanation of a passage in Yevamot 45b
that a gentile slave purchased by a Jew must be circumcised and then immersed in a ritual bath by being immersed for the sake of slavery, he takes on the status of a full slave, which, among other things, obligates him to keep certain mitzvot. However, if the slave, or any gentile, is immersed for the sake of conversion, he then becomes a full Jew and fully obligated in mitzvot like any other Jew.
Which mitzvot is the slave obliged to follow and why? For example, the mitzvot he follows must be other than just the Noahide laws, so does he follow them because he is now "half-Jewish"?