You're assuming hashrates and electricity consumption are 1:1, ignoring improvements in efficiency.

> The number of transactions the bitcoin protocol can handle is essentially capped and completely unrelated to hash rate as the difficulty of producing a correct hash is adjusted based on the hash rate.

That is true, but one must also consider that transactions & value transfer is not necessarily 1:1 either. A transaction can carry information which refers to multiple transactions, or is a transaction for a billion dollars. So value transfer is not necessarily capped, although in practice of course it is right now.

Further, to say there's no relation isn't true, either. Transactions are not dependent, but they are related to hash rates to some extent, and by virtue of the protocol this will increasingly become so, as transactions will be the main source of income that funds hash rates, there is indeed a relation.