Okay, so intentionality is essential to information. Let's take your example of the pixels on your screen.
There is nothing intrinsic to those pixels or that arrangement of pixels that points to the state of your brain. That doesn't mean there isn't a causal history the effect of which are those physical pixel states. It is, however, entirely a matter of convention how those pixels are arranged by the designers and how they must be interpreted in conformity with the intended convention. You must bring with you the hermeneutic baggage, so to speak, that allows you to interpret those pixels in the manner intended by the designers. Those same pixels will signify something else within a different context and it is the observer that needs to have the contextual information to be able to interpret them in conformity with the designer's intentions. Furthermore, the designers of the program could have chosen to cause different pixels to light up to convey the same information. They could have instead caused those pixels to resemble, in aggregate, English language sentences that, when interpreted, describe the image of the state in your brain. But there is nothing about those pixels qua pixels that can tell you anything about your brain state. The meaning of each pixel is just that it is a pixel in a particular state, and the meaning of the aggregate of pixels is that they are an aggregate of pixels, each in a particular state. You can call that supervenience in that the meaning of the aggregate follows from the meanings of individual constituting pixels, but none of that changes the fact that the pixel states as such, whether individually or in aggregate, do not intrinsically mean your brain state. This is analogous to written text. A human actor with some meaning in mind causes blobs of ink to be arranged in some way on paper in accordance with some convention. Those blobs of ink are just blobs of ink no matter how many there are or how they're arranged. The reader, which is to say the interpreter, must bring with him a mental dictionary of conventions (a grammar) that relates symbols and arrangements of symbols to meanings to be able to reconstruct the meaning intended by the author. The meaning (or information) is in no way in the text even if it influences what meaning the interpreter attaches to it.
As Feser notes[0], Searle calls this derived intentionality which is different from intrinsic intentionality (thoughts are one example of the latter). So I do not agree that anything abstract is happening in your panel of flashing lightbulbs.
[0] https://edwardfeser.blogspot.com/2010/08/fodors-trinity.html