In the trial scene Data reporting that he was ware that he was in a hearing to determine his status is presented as an argument for self awareness. but I think some might find that debatable because it is just Data saying words based upon the situation. The question then becomes is being able to accurately report a situation proof of self-awareness. If it is not self-awareness, then what is it? I can imagine a clearly non-conscious entity being able to accurately report its circumstances if the reporting were a simple subset of possibilities. A simple mechanical device with a detector that says "I am on the table" and "I am on the floor" could do that. There would definitely be a sense in which you could say that it's detection mechanism made it aware of where it was. The self part is harder, because it wouldn't know what kind of thing it is a thing at all. Is the ability to assert it is a thing meaningful? Nothing can be asserted at all if it is not a thing. Does something need to know that you have to exist to consider if you exist? Is that is what is required?
This is a difficult field. Any simple answer you hear will almost certainly be wrong.
Data didn't just describe the situation, he accurately assessed what is at stake for himself and what the consequences might be. He recognised his life and his entire being may be in real danger. Recognising that requires understanding of the "self", as in Data demonstrated he knows and understands the difference between himself and other beings/things. He is aware that he is a separate being with autonomy, and that this being of self may end. That goes far beyond just describing the situation.
As Picard repeated, “my rights, my status, my life”