In reply to Blue Straggler:
> Where is the microphone?
She's wearing a headset radio mic. It's right in front of (and slightly to right of) her mouth. Miming or not she's almost certainly wearing in-ear monitors too, though I don't think it's possible to see them at any point in the video.
> How is the multitracked vocal and harmonising working?
The backing vocals (and the instrumental band) are pre-recorded. During the bits where she's heavily multi-tracked it could be that her vocal is just one part relatively low in the mix, or it could be that she isn't singing audibly at all. Either way I guess she'd get to slack off the singing for a few seconds there.
There are a couple of other points where her mic clearly is live - the grunt and breath when he throws her onto the bed at about 1:30, the crack of the table breaking towards the end is just about audible, and at the end she's obviously (and audibly) breathing heavily.
> but unless I am a bit behind on audio technology
I think you must be, there's no technological reason it couldn't be a live performance and hasn't been for many years. All that's required is a pre-recorded backing track and one small and reasonably reliable radio mic.
It would be possible to fake the bits that convinced me she's singing live I suppose but unlikely and a bit pointless, can't really see it.
I have a small amount of professional insight here btw - I used to earn a living as a sound engineer on touring theatrical musicals. Several years packing everything at the end of the run then setting the system up again in the next venue on the tour, and the odd stint as a (competent, but not particularly good tbh) operator pushing faders on the FoH mixing desk.