One thing the press got right is that he scored a lot of goals. Almost everything else has been wrong.
The first season was framed in two phases. The early adjustment, which the press characterized as struggling. The late surge, which the press framed as proof he had figured out La Liga. Both framings missed what was actually happening, which was that he was playing his first season at a new club at his typical level and the team around him was figuring out how to use him.
The second season has been more interesting and more poorly covered. He has been used differently. He plays more from the left now, with Vinícius rotated wide right when both are starting. The combination has worked. Real Madrid has been the most consistent attacking team in Spain. The defence has been the issue, which is not Mbappé's department, which the press has consistently failed to communicate clearly.
The expectation that he should win a Ballon d'Or every year now that he plays for Real Madrid is the most foolish framing of the entire arc. Real Madrid did not win the Champions League last year. PSG did, which is why Dembélé won the Ballon d'Or. Mbappé is currently fourth in this year's voting if my reading of the panel is correct. He should be third. He will probably finish second behind Yamal.
What he has actually done in two years is establish himself as a Real Madrid player whose career arc no longer depends on French expectations of him. The French press still writes about him as a French symbol. The Spanish press has slowly stopped writing about him as a Spanish acquisition and started writing about him as a Madrid player. The football has caught up with the geography.
He is twenty-seven. He has another seven good years. The press will spend those years writing about him as a disappointment unless he wins three Champions Leagues in a row. The actual career trajectory will be more ordinary and more impressive than the framing permits.