Aren't you just describing an input-based theory of value in your first statement (as opposed to a Riccardian theory of value where price is determined by demand relative to supply)? I was under the impression that a labour theory of value is a rather specific kind of input theory since it would not treat energy as a legitimate input but instead require the value of energy be determined by the human labor required to produce that energy--i.e. the value of bitcoin should be determined by considering the amount of labour required to produce the energy required for mining plus the labor directly involved in running and the Bitcoin network. Consider a contrasting input-based theory of value which instead of using labour uses some finite resource (or collection thereof) like barrels of oil as its unit of value: here the value of Bitcoin would be determined by the number of barrels of oil required to produce the energy required to mine bitcoin. Even though it uses energy as a means of determining the value of bitcoin, this second theory of value does not involve considerations of labour at any stage.

Also (as an aside irrelevant to my above question), I think you greatly overestimate the number of people who subscribe to a labour theory of value. Personally, I don't recall encountering people who subscribed to it other than far-left shitposters on twitter (who are definitely a minority, although a rather vocal one).