i fear if you dont know how adrien and chat noir could possibly be the same person you dont understand his character
if you think adrien's "true self" is chat noir you dont understand his character
adrien agreste is a mask, that much we all understand, to be something he is not, to be in between the lines of perfection, to stand upon a pedestal for all eyes to see and he must bear it
chat noir is also a mask, (and not just the literal one) he is over the top, he is silly, he is everything adrien agreste cant be, the complete opposite of him, always being portrayed as a angel, white everywhere, and chat noir is shrouded in darkness, a little mischievous thing
adrien agreste isnt "adrien" and neither is chat noir, its similar to how parents deprive their children of something, like sugar and when that child has access to it, they go overboard, but that doesnt mean that's "them"
he's neither, both are a mask to hide whats underneath, whats underneath you may ask? nothing. because he hasnt found himself yet, he doesnt know who he isnt because he's too busy with these masks
though that doesnt always mean he's nothing either, there's traits to him that stick, even in both sides of the mask, he's kind and patient, even as chat noir comforting ladybug in her worst moments, he's silly and tells puns, even as adrien, because he cant help himself around his friends when he's having a good time
he's 14 and has been pushed into this one role for so long and then when he's able to escape he goes crazy with it, he just needs time to find himself, he's young, he will get there, but dont think that he already found himself as chat noir just because he enjoys it