Let's get simple here.
"To start with, Peter is primarily concerned with a manner of thinking or demeanor in regard to Developing a Plan"
You see this phrase all through the writing. The point is to connect and set a relationship between two ideas. One is the class.
I have no idea what it means, used in this way.
I dug into the phrase:
Referring to; concerning--dictionary.com had these synonyms, and preferred this form:
"With regard to the particular way Peter thinks, he is developing a plan." Ok, that helps. Now I understand that he's developing a plan that is characteristic of how the thinks, and not how someone else might think. If you read 'in regard to' the wrong way, you start to wonder, "is he developing a plan about the way he thinks? Is he thinking about developing a plan? What could this mean!?"
(It's actually conceptualizing -- you have an idea, and now you come up with a way to actually implement the idea. I need light - what about a light emitting glass tube? It should be shaped somewhat like a testicle, or possibly a tulip bulb -- hmm, a light testicle? Nooo... I know! let's call it a light "bulb! They'll sell like hotcakes!"
Anyway now I can see that "the way Peter thinks" is a way to characterize his planning-coming-up-with style.
Another way to say this is:
Peter comes up with a plan that is characteristic of the way he thinks. No one else would come up with this particular plan in this particular way.
"... Kate will respond with her own strengths in regard to Instinct."
Kate will respond with her own strengths in a way characteristic of her instincts. Her instinct is launch a colorful attack, so she'll probably respond that way. Her instinct is to find a weakness and instead of attacking directly in conversation, to destroy someone else's reputation with her superiors. She has read The Art of War.
Examples taken from the Relationship Throughline Character Report.
I've been tripping over this phrase for awhile and just sat down to think about it. Hope this helps someone else.
NOTE the phrase is used a lot in the generated report probably because the writers wanted to mix it up not not use the synonyms concerning, referring to, so much they wore them out. Also, because it's really just a template of language, and not much AI, they wanted a generic phrase that could plug into as many examples as it could, so they preferred vagueness to a phrase that looked awkward or just didn't fit. Just my guess.