The second part of your question is answered in the video: police/FSB came to the hospital and snatched his clothes to do the cleanup.
The first part we'll never know, but he really has no security and it is known that he's always the only tenant of his hotel room. Might have come into his room in the morning and sprayed them with Novichok while he was showering.
While he was in the bathroom? That's too risky. You don't stay 24/7 in your hotel room, do you? And when travelling for a few days, you must have spare underpants in your suitcase in your room, right?
Product idea: secure suitcase with a camera that shows people who've tried to open/tamper with it while you were not there.
It'd be interesting if the hotel staff can be questioned about government agents demanding access, but maybe the staff/eyewitness has since been "neutralized". Or if the agents were sophisticated, they'd have used widely available exploits to clone hotel keycards. Or just pick the lock. The guy on the phone even said they only go in when they know it's secure, i.e. after the cameras have been switched off.
> you must have spare underpants in your suitcase in your room, right?
I forgot to mention, that it must've been one of their jobs to figure out which pair of underpants he will be wearing the next day, i.e. which pair from presumably a few he had in the suitcase is the last clean pair. Ah, the glamorous job of a KGB/FSB agent.
Interestingly, I wonder if it meant he could only be targetted the day before he got on a long plane trip... otherwise he might put on the pair too early, get sick while still on the ground, and manage to get to a hospital.
The first part we'll never know, but he really has no security and it is known that he's always the only tenant of his hotel room. Might have come into his room in the morning and sprayed them with Novichok while he was showering.