This conversation isn’t moving forward because we’re repeating ourselves.
Halo 5’s Cortana wasn’t sane, she believed what she was saying. Cortana wasn’t trying to deceive John, even though objectively what she believed was wrong.
Halo Infinite’s Cortana is as I said, most likely glimpses of her from before the explosion (the holograms), and after (the disembodied echo voices). Cortana’s not pretending to be dead, she knows she’s irreparably broken, and she’s doing what she can to help Master Chief succeed.