It's a 2 way decision. I think we didn't show we wanted him badly enough and be prepared to spend big to get him. In return Slot didn't want to join because we didn't show we wanted him enough. Same goes for Nagelsmann. We didn't want him because we didn't agree to his conditions. He didn't want to join without those conditions met. It doesn't have to be one rejected the other. That's what negotiations are for. Sometimes both parties can't agree and then to protect their image will make it apparent they rejected the other. There's no chance Slot would come out and say he wanted to join now he's staying with Feyenoord.
Well he won't say he wanted to join us because he didn't want to join us...
In the well sourced article on the Athletic they say that Nagelsmann refused to interview for the job, didn't like the way we were set up. Spurs 100% wanted Slot but he changed his mind in the interview process.
It was never anything to do with compensation, you can believe Arne Slot would cost 10m+ if you like but it's more likely that managers are hesitant to take a job at Tottenham because they've seen how top managers like Conte can't do the job and don't want to put their career in Levy's hands.