Here is my personal experience, maybe there is something here that can help!
I have a B.S. in Civil Engineering and the majority of my experience has been in HVAC project management and energy engineering. I currently work for a large HVAC manufacturer/installer and focus on energy efficiency of commercial buildings. So, for me the entry into HVAC was through energy because HVAC systems are the biggest contributor to electric demand in most buildings. I started with the company doing Project Management for installs and renovations, and then moved into a more technical role over time.
For me, the transition from Civil to Mechanical/HVAC wasn't too bad. I don't sign off on drawings or do design at the moment, but I do focus on analyzing existing HVAC systems for proper operations and make recommendations for improvement. I actually ended up taking my PE in Mechanical/HVAC back in 2015 because I was much more comfortable with it than Civil after a few years in the industry. There was a learning curve, for sure, since I had to self-teach a lot of thermodynamics and electrical competencies. But, I would say the transition wasn't too bad.
So, to summarize, I think the main link that allowed me to move between Civil and HVAC was the Project Management aspect.