I agree 100%.
The best prep for engineering is math, at the highest level one can obtain, while still displaying mastery, Physics C, and Chemistry (it helps in materials).
This is n=1, so take it with a grain of salt. California has multiple engineering magnate schools. My son went to school with quite a few of their grads. They had a small advantage first year in the tinkering classes (joining of materials, separating of materials, additive manufacturing, etc.), because they had been exposed to the equipment. When it came to the heavy lifting though, they had no advantage. In fact, he graduated earlier and with a much higher GPA than all of his friends who had those derivative classes.
Go deep in the classics. Don’t worry about the other stuff.