help me understand the interconnectedness of this traits
Leaders need to engage their staff. To do this they need to have good emotional intelligence to understand how their staff are feeling.
Emotional intelligence is also essential for successful coaching – if the coach doesn’t recognise when people are changing, or if they can’t establish rapport with the coachee, coaching will not be successful.
One of the jobs of the leader is to develop their people, and they need to be able to adopt a coaching style of leadership to be able to do this.
So when Leadership, Emotional Intelligence, and Coaching intersect, you can get transformation of individuals and the company as a whole.
I hope this answers your question