General Case: Authority is Exercised by Individuals or Experts
The leading figure in collectivist anarchist philosophy is Mikhail Bakunin, a 19th century Russian theorist. He answers exactly your question in his work, "What is Authority?" [available here]
The work is so short that you can read it on your own fairly quickly, but this quotes summarizes his view well:
Does it follow that I reject all authority? Far from me such a thought. In the matter of boots, I refer to the authority of the bootmaker; concerning houses, canals, or railroads, I consult that of the architect or the engineer....I bow before the authority of special men because it is imposed on me by my own reason. I am conscious of my own inability to grasp, in all its detail, and positive development, any very large portion of human knowledge. .
According to Bakunin, authority is not primarily a social construct. It is based on natural facts. This is the failure of states: they attempt to impose man-made laws which are contrary to the natural order. For example, many laws could make it difficult for an impoverished person to survive - unless they break them.
Self-interest is one of those natural laws. An individual holds the highest degree of authority over themselves because they can make choices regarding their own interest.
However, no one knows enough to enact their own self interest in all matters. He uses the example of a boot maker: most people don't know enough about boots to construct or maintain their boots. So we have to trust the expert judgment of a bootmaker. Another example would be a doctor: almost no one has the requisite medical knowledge to accurately diagnose or treat their own maladies.
The bootmaker (or doctor) has authority within their own subject-matter expertise. However, the individual always has the authority to not pursue their professional arrangement any time they see fit. You could always go find another bootmaker.
So how would authority be handled? A self-interested individual would defer their natural authority to an expert. That expert then temporarily exercises authority over them in a limited way. Authority is exercised by mutual consent, and for a relatively short period.
Specifically About Labor Notes
As far as I am aware, Bakunin did not specifically address how labor notes would work. Philosophers don't generally do that kind of thing.
Bakunin also believed that the workers would collectively own the means of production. Based on that idea and the ideas in the previous section, we could reasonably expect that workers would have some "expect" in the labor note system. They could even be in a position to circulate or collect notes.
This would be different than the authority of a state (which applies to everyone) because you would only be subject to the note-expert's authority if you agreed to it. If you don't want those local labor notes, you can take your labor somewhere else. This is speculative and very general, of course.
Is it utopian?
That is fairly subjective, and left as an exercise to the reader.