Extremely silent

Wikipedia explains that pleonasm is the use of more words or parts of words than are necessary or sufficient for clear expression: examples are "black darkness", "burning fire".

I believe this applies very well here, with the caveat that I think you might be misinterpreting silent and using a definition that is not the one intended by the speaker: the word silent, when used to qualify people, doesn't have to literally refer to someone who never says a single word throughout the course of their life (that would be "mute", if anything!), but merely that they are taciturn or not loquacious – which is not a binary description.

"He is silent" could be employing either meaning, depending on whether the context involves him being silent now, or him being a generally silent person; when I see the statement "He is extremely silent", though, I automatically assume it's a description of the person's general quality of being very taciturn, and as such, not really a pleonasm at all.

Something that was pointed out in comments is that "pleonasm" is often employed more narrowly to refer to the use of multiple words that have related meanings, and even Wikipedia calls pleonasm a type of tautology, and provides examples of that type; however, the basic working definition it presents is "the use of more words or parts of words than are necessary or sufficient for clear expression". If we stopped at that, "extremely silent" would qualify (minus the above caveat).

Since just picking and choosing parts of a Wikipedia definition isn't satisfactory, I will also look elsewhere. Merriam-Webster defines it as

the use of more words than those necessary to denote mere sense (as in the man he said)

and ODE as

the use of more words than are necessary to convey meaning (e.g. see with one's eyes), either as a fault of style or for emphasis.

Admittedly, both examples involve repetition of related meanings ("he" and "the man"; "see" and "eyes"), but the definitions themselves don't. I think the examples can be explained away as the most obvious type of pleonasm that comes to mind.

I find it interesting that one of the dictionaries provided by Dictionary.com (the "British Dictionary") actually gives two separate definitions, the first being similar to the ones we've seen, but the second being a terser

a word or phrase that is superfluous

Under this definition, anything that can be omitted from communication due to being already covered elsewhere can be termed a pleonasm.

The etymological argument, for what it's worth, can also be brought forward, as Etymonline explains that pleonasm comes from πλεονάζειν, which simply means "to be more than enough" or "to be superfluous", which in turn simply comes from the root for "more" (the same root that generated Latin and English plus, I believe).

Extra words that do not provide any additional meaning are redundant. This doesn't specifically apply only to the case of adverbs in front of binary adjectives, but it is an applicable term.

If one accepts that silent is really binary, then saying "utterly silent" is redundant, because silent inherently means the complete absence of sound, and it's impossible to be more silent than that.

In reality, silent is not truly binary, because in everyday usage, it really means mostly quiet. Humans almost never encounter a condition of true silence, and usually use it to mean a general lack of sound or speech. If I say "Charles remained silent throughout the meeting" that doesn't mean there was no sound whatsoever coming from Charles, just that he did not say anything. His heart was still beating, he was still breathing, and any minor movements he may have made probably produced sounds as well.

To make a distinction between this meaning of silence and the meaning of complete lack of sound, which is extremely rare, an adverb can be added. "When the power went out, the room became utterly silent."

Extremely silent means 0 decibels

Extremely Silent 0 decibels and can't be heard

Near Extremely Silent Not inaudible or halfway between