Spurs have to grow out of appointing superstar managers and then not giving them superstar budgets. In this sense, I'd argue Postecoglou is the right caliber of manager, but I have no idea if he himself is the right guy.
I think Spurs might be a bit of a poisoned chalice just now. I think of them as having overachieved in the last decade or so, and Kane has been a huge part of that. One way or another, they will lose him soon, and then they may relapse to seasons finishing 8th, 9th, and 10th, with the occasional bottom half season. That's essentially what they did for my first 25 years or so of following football.
As for Celtic being a bigger club, who cares? Certainly not any players or managers. Why should they care? Both care about what they'll be paid, where they'll be living and what competition they'll be playing in, probably in that order. Size of club is irrelevant.