A 'participle' is a verb form that is nonfinite and an adjective or adverb. So, "liked" is certainly both a "participle verb form" and a "participle adjective" as well! Those can both be true, and are both true in this sentence.
"Liked" is /not/ a finite verb form here, and 'everybody' is not its subject!
This is a little confusing, because "liked" spelled just the same can be a past tense finite verb form with a subject, sometimes:
Everybody liked her.
Here, unlike you example sentence, "liked" is not a participle.
But in your sentence, it is a participle, and your book is correct that the use of 'much' is permitted because of this.
So, "by everyone" is a just a prepositional phrase. Compare the following sentences, which are grammatically identical:
She is liked by everyone.
The soup is cooked with wine.
It should be clear that "wine" is not a verb subject. The wine is certainly not doing the cooking. But the grammar is exactly the same in both sentences - "everyone" is not a verb subject either in the first sentence.