Considering the OP (original post here),
from my decades of experience in working
as an employee doing technical work,
computing and applied math, in
organizations, my main lesson, conclusion,
response has been just to start a
business, right, exploiting, using
computing and, for an advantage, applied
math. The computing has some mathematical
aspects but is nearly all just routine
Microsoft .NET.

A general thought is: For someone A to
have a good job as an employee, there has
to be an employer B who creates that good
job. So, if A is pretty good, useful,
valuable, etc. for B, then maybe A should
just start and run their own business.
E.g., the guy who used two old Dell
computers as Web servers, wrote software
using .NET, and, alone, built the romantic
match making service Plenty of Fish. Then
he wanted to sell, hired a lot of people,
and sold out for $500+ million. He seems
to be an example of a lot of advice
including "Build and provide something
people, maybe a lot of people, want."

So, that's what I'm trying to do -- build
something a lot of people want. Currently
my .NET code is 100,000 lines of typing
and 20,000+ programming language
statements. I got delayed by some
unpredictable, exogenous influences but am
making good progress now.

But to respond to the OP, my experience
being a technical employee is not much
like what is in the OP.

Here are some lessons from that school of
hard knocks:

(1) Don't Be Very Good. My experience is
that if work to be really good, if are
really good, even if just are seen as
working hard to be really good, that is
commonly seen as a firing offense.

Why? If you are good, making important
contributions, maybe are close to
essential, then you can get some power,
and the power can scare nearly everyone
else. In simple terms, to some extent, an
organization is a fight for power. So,
it's a fight.

(2) Goal Subordination. Business schools
commonly teach a whole course in goal
subordination. So the idea is that the
organization has goals but a lot of the
management subordinates those goals to
their own advantage in the power struggle.
So, such managers can gain while the
organization suffers. Uh, remember this
if become a manager of managers!

(3) People or Things. There is an old
remark, way too simple but still with some
truth, still approximately true, possibly
a significant factor among many others:
"Growing up, boys pay attention to things
and girls, to people." Commonly girls and
young women are much better with people
than boys and young men of the same age.
So, the girls (females) can be better at
pleasing others, at the OP's "nice to work
with". The difference here between the
genders can be extensive, say, run wide
and deep.

(4) Human Resources (HR). The OP
mentioned HR: It appears that somehow, to
a significant extent, the people in HR can
be especially skilled at working with
people and especially sensitive to the
related issues. So, some guy really good
with technical material and things can
easily offend the HR people. E.g., early
in my career I was hired under a special
HR program and occasionally asked HR about
the promised evolution of the program.
The HR response was somewhat worse than
had I been proposing to drop into boiling
oil kittens, puppies, and babies, in
particular their babies. They arranged to
get me fired. We never communicated in
English what they were upset about, but
still they worked hard to get me fired.

In my decades of experience, more
generally, commonly in practice "easy to
work with" is more about manners in a
Victorian Royal garden party than anything
about the actual work. Or maybe borrow
from a politician who wants to make sure
never to offend any group, even a small
group, even just one person so always
speaks in highly ambiguous statements
about widely accepted thoughts, positions,
etc.