Being + P.P construct as progressive form of -ed participle or passive form

Being worn out from all the work, John decided to relax for the evening.

While this sentence is grammatical, I disagree with The Grammar Book's interpretation. "Worn out" is not a participle in this sentence; rather, it is simply an adjective (Source 1, Source 2). This being the case, the phrase "being worn out" is a participial phrase (Source 1, Source 2, Source 3). Participial phrases act as adjectives. In this case, the phrase is describing the subject of the sentence, John. "Being" is the present participle of "to be", not a helper to another verb, and "worn out" is the subject complement. Who is worn out? John is worn out.

I agree with The Grammar Book in one respect: the use of "being" does emphasize that John's "worn-out-ness" is the "reason or cause for the result expressed in the main clause", i.e. deciding to relax.

---

Being consulted on the matter would have been nice too.

This is also a grammatical sentence, and it is undoubtedly an example of a passive voice construction. The implied subject of the sentence, "I", would be the object of the verb in an active construction.

Note that the use of "being" here is a specific case of a general principle. We create passive-voice constructions in general by pairing the past participle with various tenses of the verb "to be" (Source 1, Source 2).

Active Voice:

They consult me on the matter.

I consulted Terry last week.

Consulting me would have been nice.

Passive Voice:

I am consulted by them on the matter.

Terry was consulted by me last week.

Being consulted would have been nice.

---

In short, the first example is not a case of "'being' + [past participle]" at all, and the second example is a specific case of "[form of to be] + [past participle]".