Here's a related discussion, in which my answer points out 'pure reason' cannot provide motivations, or values The illogical nature of want/motivation and its effects on free will
One of the primary roles for emotions is coding memories. Extreme emotiinal states link us to other experiences, and the things we learned there, and put relevant 'shortcuts' to responses up like fight-or-flight. Other subtler emotional states or modes of behaviour or action, similarly help us link to areas of what we know. See the role of the amygdala, and emotion and memory.
I would look to Kahneman's Thinking Fast And Slow to understand emotional responses are often 'good enough' intuitive reactions, until something triggers the need for a slower reflective more resource intensive reaction. I'd say this area is the source of the idea of a binary between logic and emotion, and of the different activated areas in the article you link. This is a great book, and his research behind it won him a Nobel in economics. I'd also look at the Dunbar Number and the expansion of the prefrontal cortex for social inhibition of emotions, in relation to our social self. Vs the 'flow state' of loss of self in demanding skillful physical activities like elite sports. The Deafault Mode Network is also related to maintaining this social-self, and the work of understanding the intentiins of others.
AI research is starting to look at programming emotions, like doubt. Because a command like 'get me a cup of coffee as fast as possible' might involve killing people in the way to the coffee, but a human would understand relative weighting of different priorities, and know when to doubt how categorical commands or statements are even if their true meaning can't be deduced.
Another way to reflect on emotions is cognitive bias, and post hoc reasoning. In thisnperspective we develop tools to mitigate our biases, often systematically, and to investigate and correct for assumptions. I'd say this area is the source of the idea of a binary between logic and emotion, because it focuses on tools developed to address problems with our quick 'emotional' reactions. But we may learn to 'trust our gut' or other ways to cultivate intuitive emotional responses, as well responding by analysing.
Emotional Intelligence is a way of thinking about, how we use and relate to emotions, can be developed. Things like secure attachment, and a growth mindset, can be understood as bolstering useful healthy emotional responses. Here I make the case that the cultivation of wisdom is basically a kind of cultivation of emotional intelligence, once focused on dealing with internal conflicts and contradictions, towards self-knowledge and so better solving dilemmas Wisdom and John Vervaeke's awakening from the meaning crises? It is notable that our modern culture barely mentions wisdom, but puts great stress on intelligence. But wisdomWisdom has always been seen as integrating intelligence and emotion, as involved with holistic answers and outcomes, correcting 'pure' or cold intelligence.