Cut the wires and splice in the new dome light. Click or replace all the wire.
Wiring diagram says ORN and WHT but who knows what has been done by previous owner. Does not make any difference which new wire/color goes to which existing wire/color.
BUT not sure what the problem is.
Trying to get the whole assembly out to replace with a new one and the wires are holding you back?......or can't get the socket housing to come loose mechanically