The following is my attempt to interpret the passage in its context.
Jews originally possessed SOME rights as CONQUERED people in their enclave, but nothing like autocracy, denoted by authentia. However, the Jewish priests humiliatingly refused to allow “god” Ptolemy entrance beyond the Court of the Gentiles into the Court of Israel, in order to offer HIS gift. Ptolemy’s stated intent in revenge, was to humiliate all the Jews – who were allowed in the Court of Israel – and to prohibit them from making THEIR gifts. He decided to give them the choice of death or to become slaves deprived of freedoms. He was not going to leave them exactly as they were, “set apart with these limited rights,” being to some degree masters of themselves. They were now not able to sacrifice in their Temple in Jerusalem, thus also no longer demoting him beneath their God. They could not enter to make burnt offerings, thus ending both the many free will offerings, and more crucially, the atoning sacrifices of Judaism. They could merely enter for prayer. However, if they also agreed to bear the publicly humiliating branding mark of a foreign god … as servants of himself and the god Dionysus, no longer just the servants of YHWH, then they would have “authority to kill” i.e. be allowed to sacrifice, but with those degrading conditions attached.
These more draconian measures seem more in keeping with the commentary of v 30a, “To do away with the appearance of hating them all.”
The logic of the whole inscription is: “If you want to pray to YOUR God, you must become my slaves – or die. If you want to sacrifice to Him as well, you must also be branded. But if you agree to worship MY gods (and myself) you will live as free people, with equal rights as Alexandrian citizens.”