Both "are" and "is" are tenses of "be", and "be" can mean several things. The definitions of "be" (from Merriam-Webster) we are concerned with is:
D: to have a specified qualification or characterization
Your first and third examples are:
Book A and Book B are red.
Book A is red and Book B is red.
This is the English language equivalent of the distributive property. If Book A and book B are red, then I can distribute the verb and adjective to both while conveying the same meaning. Instead of a compound subject, I now create a compound sentence. This is exactly what you describe in your question.
Your second example is:
Book A and Book B are similar.
"Similar" describes a relational characteristic. You cannot distribute "similar" to apply to each noun individually (without additional context) because it requires two objects to form a comparison.
To explain in CS terms, think of it as "are" being a token that relies on the following token to define its own behavior.
Certain following words may define characteristics of each of the preceding nouns:
These books are expensive.
Others may define characteristics between each of the preceding nouns (
These two are lovers.
Lack of a following word may describe its inclusion in a previous statement
Which books are on sale?
These books are.