I cannot claim to be an anything close to an expert on Dr. Shannon's theory; however, Shannon's work seems to center on the concept of "information" as represented, for example, by bits -- a pair of binary states that can be represented in various ways: the position of a relay, for example, conveys one "bit" of information.
In the real world, a "bit" is physically represented in various ways, and those bits are transmitted by various physical means -- modulated onto an RF carrier, for example.
Shannon's paper (to which you provided a link) deals in various ways with the topic of encoding and decoding information onto a medium, in the presence of noise.
Shannon makes no assumptions about how the bits themselves were defined: he merely addresses the bits themselves, and the likelihood of recreating or approximating on the receiving end, those bits that were originally placed on the carrier at the transmitting end.
Position, mass or energy, charge, whether it is a fundamental entity or comprised of other entities and how we can tell what is not information.
Given that we work with Shannon-type information every day, it is quite evident that "bits" are not simply abstractions -- they have very distinct physical meaning as well. And yet they're also "representational" in the sense that various physical methods can be used to represent the same (say) binary state.
What you're digging for, apparently, is a statement that the interpretation of bits is the same as the bits themselves. But that's just it: if we want to talk about "information" in a Shannon sense, we are merely discussing the likelihood of faithfully recreating the transmitted bits the original bits, after noise has altered the state of some portion of the transmitted data.
Shannon's work doesn't deal with intent on the transmitting side, nor does it deal with interpretation on the receiving end -- it merely deals with the data themselves.
These will be possible signals for the channel. Thus in telegraphy suppose the symbols are: (1) A dot, consisting of line closure for a unit of time and then line open for a unit of time; (2) A dash, consisting of three time units of closure and one unit open; (3) A letter space consisting of, say, three units of line open; (4) A word space of six units of line open.
As you can see the signals are represented on a physical medium but they are defined conceptually. A dash could have been defined as consisting of four time units of closure and two of open.
Also, the term "information" has morphed in common usage to mean the message itself, which upon receipt in measured in bits.
But information under the Shannon model is the reduction of uncertainty (Shannon entropy) in the receiver as it moves from a before state to an after state. It is the action of successful communication, not the message itself.
So whereas the receiver's having being informed (reduction of uncertainty) is quantifiable providing the before and after states are measurable --- both the received message and the information (action) may be physically manifested (subject to observation) - or not.
For instance, a voice message and the pressure wave whereby it arrived are physical and observable.
Conversely, a Spiritual truth and the manner whereby a Christian is "informed" are not physical. Even so, the "reduction of uncertainty" in the Christian is real, and if his before and after states were observable and measurable, it could be quantified under the Shannon model.
But the natural man receiveth not the things of the Spirit of God: for they are foolishness unto him: neither can he know [them], because they are spiritually discerned. – I Corinthians 2:13-14
In the beginning was the Word [Logos], and the Word was with God, and the Word was God. The same was in the beginning with God. All things were made by him; and without him was not any thing made that was made. In him was life; and the life was the light of men. – John 1:1-4
Why do ye not understand my speech? [even] because ye cannot hear my word. – John 8:43
But ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. Now if any man have not the Spirit of Christ, he is none of his. – Romans 8:9
Personally, I see the unreasonable effectiveness of math (Wigner) as God's copyright notice on the cosmos. And that includes not only geometries and functions but also "information theory and molecular biology."
As a final note, the earliest cosmic record of a pressure wave (sound) is recorded in the cosmic microwave background radiation at the moment light formed and went its way.