It is true that Newcastle are not a very big club to attract prominent managers like Klopp. But maybe they can give him a promise like they will bring world star players to the team. They have the money power to make it happen in the end. They have no problem with money. And I'm pretty sure that Newcastle will build a great team especially for the next season. In that case, the most needed thing will be a good manager who can carry the team to big successes.
Big players have other demands also apart from big money like good repute of club, good coaches and managers, titles won, sponsors etc. They only made switch based on such parameters. Its just the start, I am sure the new management has lots of money and money can bring everything. Remember the Man City take over by UAE prince help them won there first title in history.
Besides, they are after the players like Werner, Süle and Coutinho. These transfer targets are for the January transfer window as far as I know. Even after the winter transfer window, they can have a really solid lineup as it seems.
The player does not choose between "favorite club or money", all proposals for money are approximately at the same level (the market is efficient), but money is one (albeit the most important factor) from several decision-making factors, there are also prospects (it is obvious that with Real Madrid the prospects are better than with a newcomer club among the top clubs) and country of residence (here I do not know anything about Mbappe's preferences). 
