Como dizer "ficar na sombra de alguém" em inglês

I would say, "He grew up in his brother's shadow" or "He grew up in the shadow of his brother."

There is a subtle difference in my perception. In the case, "John grew up in the shadow of his brother," the meaning is that John was overshadowed by his brother. No one could see John because everyone was focused on his famous brother. The emphasis is on the dark shadow, growing up covered in darkness. And the brother outshone him.

In the case "John grew up in his brother's shadow," it was not as severe for John. It could be a positive thing to be able to follow in the footsteps of a successful, knowledgeable guiding brother. The shadow can be protective, as the shade of a tree protects us from of an excessively hot sun. In this case, growing up in his brother's shadow shielded John from the harsh, blistering, difficulties that the brother faced, and John was spared (escaped) the same struggle by following in his brother's footsteps.

Examples from the internet:
John Faulkner has never been viewed as a significant figure in literary history, possibly because he grew up in the shadow of his brother's fame.

He grew up in the shadow of his three older and more successful brothers, Frank, Howard, and John, who tormented and bullied him.

Google turns up 2.730.000 hits (results) for he grew up in the shadow of his brother
And 3.340.000 páginas em Inglês sobre he grew up in his brother's shadow

I have more or less the same reaction as you, Mary.

Fico com a impressão, por exemplo, de que a expressão "follow in the shadow of" é usada geralmente num contexto positivo.

Rest saber qual tratamento Anita quiz dar a essa expressão.

Regards