There does not exist an expression of "in the way" when indicating some kind of choice, opinion, manner, right?

Question

per Cambridge dictionary (https://dictionary.cambridge.org/dictionary/english-chinese-simplified/way), there is only 2 expressions "in a way" and "the way" when indicating some kind of choice, opinion, manner, "someone's way" could be considered as "the way".

It's amazing the way she manages to stay so calm.

In some/many ways it would be better if we met on Monday rather than Wednesday

There does not exist an expression of "in the way" when indicating some kind of choice, opinion, manner, right?

Answer 1

It seems possible to me, and google finds some examples:

It lies in the way that she has resisted racism and sexism to survive “in places where there was no light, no food, no sisters, no quarter.” [source]

She had committed herself to make satisfaction for many sins in the way that she has said. [source]

Kabango-Kasale has shown exemplary leadership in the way that she has given women and men equal opportunities within her media house [source]

This would seem to just be the usual combination of a preposition and a noun, and not a special idiom.

Answer 2

Your two examples contain two different definitions of "way":

1. a method, style, or manner of doing something; an optional or alternative form of action.

2. a particular aspect of something

You should find these two distinct definitions in any good dictionary.

Your examples:

It's amazing the way she manages to stay so calm.

Here, "way" refers to the method or manner of which she stays calm.

In some/many ways it would be better if we met on Monday rather than Wednesday.

Here, "ways" refers to different aspects of the reason why Monday is better than Wednesday.

---

I'm not fully sure what you mean by using "way" in connection with a choice or opinion, but when you choose to go a particular direction, it can be described as going a particular way - not just literally moving in a particular direction, but also figuratively, following a course of action:

He chose to go one way, I went another.

That is certainly one way of doing things.

In these examples, the first dictionary definition I quoted above applies, so is not really any different to your example.