Your research is correct so far as it goes. There is more that can be said about brew.
to make beer
verb intransitive or transitive
If you brew tea or coffee, you add boiling water to it to make a hot drink, and if it brews, it gradually develops flavour in the container in which it was made
Brewing beer or hot drinks takes some time as various reactions occur and flavours develop. From these meanings comes the idea that something can be prepared so as to develop slowly. This gives us the idiom of:
If an unpleasant situation or a storm is brewing, you feel that it is about to happen
Or we speak of brewing a cold when developing a cold.
The brewing does not necessarily have to presage something unpleasant. Going back to the original meaning of preparing beer or a drink, it may be something pleasant or neutral. Hence your example of brewing a conversation, which refers to gathering the thoughts and ideas (and perhaps the people) necessary to start and continue a conversation.