I would say the "but" is absolutely necessary, and the "also" is not: it can be replaced by "as well", "in addition", or even nothing at all.
She found herself in a completely different place, ...
... not only in terms of culture, but also in terms of climate.
... in terms not only of culture, but of climate as well.
... not only in culture, but in climate.
And so on.
Student or Learner