Designing an abstract icon system [migrated]

I'm trying to design a small universal abstract icon system comprised of at most 10 unique icons.

The goal of this icon system is to uniquely identify something without inducing meaning.

It is to be used where no traditional icons set could cover the meaning desired.

As an example: Let's say you have an app for the bird watching community where they can report sighting of different kinds of birds on a map. Each marker on the map would have an icon to identify the species of bird. Here, the meaning of the icons is very specific, no icon sets could cover their needs (even the material icon set probably has just one "bird" icon).

What is needed here is a icon set that just uniquely identify type of publications (types of birds). It it then the role of the app to give meaning to these icons.

Be abstract

The icon system is to be used in different contexts. The icons therefore can't convey any particular meaning (e.g a heart icon can't work has it a strong connotation to "liking", or "favorite"). This means the icons needs to be abstract. An example of abtract system would be to use colors.

Be unopinionated

If colors works for the abstract part, it would also cause another problem. Colors are opinionated. Meaning if we give the users the ability to choose between 10 colors, the distribution of choices will not be equal (more people will pick blue than brown for example). The system, therefore, has to be as unopinionated as possible.

Be as recognizable as possible

As the icon set to be used in different contexts. Icons need to be as unique and differentiable from each other (for example if displayed super small).

Be referable

As the icon in the set are abstract. There is no easy way to refer to an icon by name. A naming system, therefore, needs to be developed to go along with the icons to make them referable (e.g. "Oh, just use the X icon")

What i've tried

Colors

Colors are great. They tick almost all the boxes except they are very opinionated. I wonder if there would be a choice of palette that would be less opinionated ?

Geometric shapes

Geometric shapes work as well. They are abstract enough and referable by name. However, there is not enough easily differentiable shapes (after all, everything is just a variation of the 3 basic shapes circle, triangle, and square)

Emojies

Emojies are great at conveiing specific meaning and are universally understood. However, their strength come from the fact that there is thousands of different ones available, that is not compatible with our limited icon set size.

Complete randomness

The idea would be to create an icon set where every icon is a complex random abstract shape and associate it with a completely random name (like "orbe" or "fungulus").

In principle, this would tick all the boxes but require A LOT of education to make it usable in the real world.

I'm sure this problem has been tackled many times (it might even be a science of its own) but I can't seem to find any resources online.

So if anyone has an idea of what to look for, or even direct ideas or suggestions, I'd be very grateful, cheers! ;)