It seems like you assume that there's a true platonic form that corresponds to the word belief instead of different models of belief being useful in different contexts. It's unclear to me why one would believe that to be the case.

An understanding of part of reality.

It's very unclear in what way this is supposed to be helpful. What understandings are there that are not understandings of "part of reality"? Without making that clear you just exchanged the word belief with understanding without having moved forward at all. 

Whether or not beliefs come in degrees is an empirical question. I'm very skeptical of pretending that it is no empirical question. 

Generally, in science, you solve an empirical question like this by having an operationalized definition for your concept and then measuring in reality what that concept does. Leverage Research for example developed with belief reporting a tool that operationalized beliefs and you can empirically study those beliefs. 

There are also some hypnosis tools that can be used to make interesting experiments about what effects changing beliefs has. 

That is, I believe that these biases are simply logically inevitable features of reasoning for any form of intelligence. 

If what you think what you are saying applies to all intelligences, do you hold that GPT-3 has beliefs? If so, it might make sense to focus on it, given that it's a lot easier to experiment with it than with humans. 

The beginning of chapter 1 introduces a definition for the word "belief" which is very specific and not close to the common everyday meaning.  The concept you're talking about has no specific intuitive word that would be better to use, so "belief" is as good as any (IMHO) but I think you need to spend the first page or two examining what you mean by "belief" and relating your concept to existing concepts in neuroscience and psychology.

In the real world, understanding of the universe changes incrementally.  So starting out by telling the reader that everyone else is wrong and you have the "true" answers is bound to make people stop reading.  In order to sell a book to a publisher you have to make some kind of wild claims about the significance of your ideas, but I would write the book first, and leave the wild claims as a last-minute addition to the book cover. (grin)

The concept you're talking about seems to include the entirety of our apprehension of ourselves and the world.  The most common words that I could think of that come close to this idea were:

 - feelings
 - beliefs
 - understanding
 - knowledge

In other words:
Not memories, but the sense we make of our memories
Not sensory input, but the sense we make of the input

For example, the following ideas would be considered to be part of this concept:

 - I am bad at math
 - My math teacher is mean
 - There is no milk in the fridge
 - The sun will rise tomorrow
 - People have the right to privacy
 - 2+2=4

If you gave these examples to a group of people and asked them to pick one of the four terms I gave, you would probably not get consistent answers about which ones are beliefs, feelings, understanding or knowledge.

Much of our the beliefs that we express are retroactively justified.  You may want to read this fascinating book on the nature of consciousness: The Mind is Flat by Nick Chater

https://www.theguardian.com/books/2018/mar/22/mind-is-flat-nick-chater-review-hidden-depths