I think Federation is the most appropriate faction to represent AI rights.
I imagine New Empire policy in regard to AI is subjugation, oppression, and slavery. Partially because Empire fought an all-out war agains the Machines, and partially because most of Empire leadership was what is now Dynasty.
That is, unless new leaders say otherwise, the remaining two factions' discussion of AI politics is whether AIs should be mostly lobotomized or mostly exterminated.
I imagine Federation as the backslash against the authoritarian Empire taking over every neutral world on the map, with the remaining few deciding to put their differences aside and restore a galactic republic of sorts. Such a polity wouldn't have much issue also supporting limited AI rights.