I agree with your final 2 paragraphs.

>that adjustment . . . can also be compensated for by change in the price of bitcoin.

It can. When I wrote that if the mining reward is cut in half, the electricity consumption of the network is cut in half, too, I assumed that the price remains constant.

A miner must pay for the electricity he or she uses. Where do you think the money comes from to pay for the massive amount of electricity used by the network?

Do you imagine that rich people (i.e., people who can afford to lose money) are buying the electricity for pro-Bitcoin ideological reasons?

I don't: I believe that it comes out of the revenue made (collectively) by the miners. In other words, the payments for the electricity are parts of (individual) plans to make money through mining.

And I believe that if that (collective) revenue were cut in half -- especially if miners and prospective miners knew of the halving in advance (particularly, before they decided what mining hardware if any to buy) -- then money spent on electricity is approximately cut in half, too. (Because otherwise the plans to make money would not work.)

You are correct that the adjustment in the hash rate is not immediate after a halving of the mining reward. Mostly that is because miners who recently bought mining hardware have to continue mining after the halving to continue to pay for their hardware.

If the halving was announced in advance, then the halving will start exerting downward pressure on the mining difficulty months in advance of the actual date of the halving. The major cause of that downward pressure is miners opting not to upgrade their hardware and prospective miners opting not to enter the mining business in the first place (the effect of which is to make it take longer for the remaining miners with their non-upgraded hardware to solve the proof-of-work puzzles, which in turns causes the software to reduce mining difficulty to return the average time between successive blocks back to 10 minutes).

Basically, it takes many months for newly-manufactured mining hardware to pay for itself, and that delay is the main reason the response to a reward-rate halving is slow. But again the response starts months before the actual halving; and the cumulative effect of the halving on the rate -- more precisely the effect the rate has on how much electricity is consumed by the network over the years -- is approximately the same as it would be if the effect of the halving on the rate were instantaneous.

It is the fact that one of the major expenses (namely, hardware) of the miners is "lumpy" (requires an upfront expenditure that is then recouped over many months) that obscures the simple relationship whereby the collective expenses of the mining community approximately equals the collective revenues of that community -- where most of that revenue is from mining rewards, which is equal to the price of bitcoin (or the value of bitcoin if you prefer) times the rate at which the network dispenses bitcoins from miners as rewards. What makes me confident that expenses = revenues is that miners are rational and consequently are capable of taking into account scheduled halvings of the rewards to mining and the "lumpiness" of the cost of mining hardware (and many other factors).