I think you missed my argument.
Your specific frame of reference is called 'scientific materialism', it's been around since the Enlightenment, and like any metaphysical frame of reference, it requires it's own basic assumptions. For example: "The universe is made of this stuff we call matter and energy and those behave according to a specific set of laws". This is unproven, unverifiable etc.. (By the way, you snuck one in there 'information' - which is an abstraction).
It's a useful tool, but it has some problems.
For example - in the context of scientific materialism - we cannot even be 'alive', let alone have 'intelligence' or have 'morality' if we are merely a bag of randomness. A bag of random particles in the Universe must be random at every level.
Here's a paradox for you: "prove to me that you are alive". Basically, you can't. Life is the most important thing there is, and yet we don't even know what we is. If an alien being made of metal parts landed and 'asked for our leader' we'd have a hard time determining whether it was 'life' or not.
Our entire civilization and existence is framed around the concept of life, and of what is not life.
FYI - this 'gaping hole' in Materialism has given rise to kind of a new field called 'Emergence' which is the beginning of the materialists journey to try to understand how complicated interesting things seem to arise from simpler ones - though the field has no answers, the point is good because it recognizes the 'hole' I mention.
"The logical conclusion is that a soul if it did exist would be made of matter/energy/information like everything else that can possibly exist."
Not really. Humans understood that gravity existed, or how it worked very crudely, and dealt with it ... for thousands of years before we even had a word for it, or were able to characterize it rationally in any way.
We have a rough ways of grasping issues while be develop better tools.
So - I did not indicate anything to validate thousands of years of specific superstitions (chemical processes, or magical cures etc.). But the fact that there are words for 'Spirit' 'Soul' or 'Animus' etc. which have developed independently across cultures over various civilizations is a pretty strong reason to indicate that 'something interesting is going on there'.
It's funny because when one steps back for the very specific and narrow view of Materialism, it's an easy concept, it's just that most people are conditioned to narrowly accept current interpretations of 'energy, matter' etc. as 'Truth' that it's hard to consider another view.
The 'hand waiving' is made by those that simply make up and invent premises such as 'The Universe Is Made Of Matter and Energy and Behaves According to Mathematically Describable Laws" - which is unproven and cannot be proven - and then pass it of as an incontestable fact, and then derive all of their arguments based on this supposition ... especially when this definition of the Universe literally denies the very existence of life.
Scientific Materialism was invented by humans do describe: the material. It should be no surprise that it starts to fail when we apply it to other, more existential concepts.
Science is not Truth. It's just a tool, an interpretation. That's it.