According to the Alshich, this posuk describes to us that there a different ways in which we can see "richness". We speak about richness when we have a lot of money, but we can also speak about richnesss when we are wealthy in other things, especially when we talk about richness in Torah.
As Rashi says:
The wealth of the rich in Torah
The Rabbeinu Bahya, in his commentary on Vayikra 5:6 explains the difference between rich and poor people, in bringing offers:
The Torah distinguishes between the rich, the poor, and the destitute. The former has to bring a sheep or goat, the person who is poor brings either two pigeons or two turtle-doves.
So, the Torah needs a rich person to bring a sheep or goat (to offer). To me, it seems that having a lot of sheep can tell us that a person is rich. The posuk describes Job as having many cattle, hence being rich.
This brings us back to the commentary of the Alshich:
A second fundamental teaching can be learned from these verses. There are two types of wealthy people. Some have material riches and an abundance of possesions. Others are rich in Torah and good deeds, but live frugally, for they have meager funds. [...] Iyyov was rich in both senses of the term. He was rich in character, for he was wholehearted and upright. He was also wealthy materially - as we see from verse 3 - and lacked nothing. Scripturem however, employs the word וְהָיָ֣ה with reference to his righteousness alone (v. 1), as only when one is occupied with Torah and mitzvos, can one experience true joy.
So maybe, the reason why the Torah leaves out the description that Job had a lot of money, I think the Torah teaches us the lesson that Job was rich in other ways.
Please refer to the Metzudos Dovid, who says that he was rich in having many assets:
גדול. בעושר ובנכסים