However, with my Voice Coach hat on, I would also say that to my ear, her breathing was a little noisy, which indicates to me that she is slightly constricted (tight) in her throat. When you can hear the breath as you inhale, you are hearing the False Vocal Folds getting in the way and causing turbulence in the airflow.
The False Vocal Folds are nothing to do with singing and all to do with closing over the top of the True Vocal Folds when you swallow to prevent food or saliva getting down your airway. If you are constricted enough to cause noisy inhalation, you may be constricted enough to annoy the True Vocal Folds, which are sat beneath the False Vocal Folds trying to vibrate hundreds of times a second to create a pitch.
Singers have to learn to 'Retract' (widen) the False Vocal Folds out of the way to prevent them from interrupting the vibratory cycle of the True Folds. Your breath intake should be silent. The sensation in your throat should be wide, like that of a hard silent laugh, or the beginning of a yawn, or a silent gasp of surprise - any experience that gives you the sensation of width in the throat. Perpetual constriction when you are singing or speaking will result in vocal fatigue and may lead to vocal trauma and long term vocal fold damage.
It was wonderful to hear Adele's stunning voice again tonight. But the voice professionals around her will need to spot what was going on tonight and support her in keeping her voice use as healthy as possible. After her triumphant Grammy & Brit wins, she's got a lot to sing about...