I think Tai Sabaki encompases all the aspects of the physical body movement you do during a technique. This includes stepping, centering, leading, etc. This would not include things like breathing, energy flow or doing something in isolation like using arms and shoulders without your complete body being involved.
Our Shihan sometimes has us do excersises and will say no tai sabaki because we are just doing a grip strength thing or practicing kotegaeshi hand work.
He also complains the most about our poor tai sabaki and not doing enough tai sabaki while doing techniques.
It can be confusing because I would like to know what aspect of tai sabaki is lacking for example not centered enough? or maybe didn't use enough hip?
I believe it is highly important in our training.