I cannot work out whether that Mail link is just badly written, or they are confused.
In the week of the by election in Hartlepool, it is perfectly reasonable that the Labour Leader and Deputy Leader used the same local office. There are loads of photos of Starmer anf Rayner campaigning together there such as this one widely published at the time.
https://www.indy100.com/media-library/keir-starmer-visit-to-the-north-east.jpg?id=28061140&width=1245&quality=85&coordinates=0%2C137%2C0%2C137&height=700
Of course they were in Durham together.
The Mail publishes a photo of her waving at them (presumably from a different location). She was either on a conference call or doing the online quiz, but from another building.
She does not appear in the video of Starmer drinking from a bottle.
Looks like a desperate attempt to concoct something out of nothing.