After leaving Roma, he didn't go to the Saudi league, but Mourinho. If he really wanted to, he would probably be managing a team in the Saudi league now. I don't think he wants to leave Europe. I don't think money is a priority for him. Also, they didn't sign Lukaku, but Dovbyk came and I think he is a striker who can do good things. His presence is more important for Roma than Lukaku.
I also think that money isn't a priority for him, he has nothing to do with money if maybe he isn't happy. I waited to answer you to understand Mourinho's motivations a little, maybe he doesn't like the league or maybe he really loves staying in Europe. I honestly don't know the motivation behind this choice.
It seems like he still really wants to be in Europe and still wants to prove that he can still compete with other younger coaches. He is a very ambitious person, even though we know that he is a coach with controversy that he always does, but he can cover it up with achievements too, or in other words he is arrogant and can also prove what he says. Or he deserves to be arrogant even though sometimes it is annoying. Lol
Regarding the new AS Roma player, he is the player who scored the most goals in the league he played before. AS Roma is very lucky because they managed to get his signature, because this player is also in demand by many clubs, but he prefers to join AS Roma. Even though if he wanted he might be in a bigger club than AS Roma. Now AS Roma only plays in the European League, even though there are clubs interested in him who play in the Champions League.