"Afghanistan has no coastline and Russia has no border with Pakistan, and as far as I know, it never had much in the way of diplomatic relations with it, either. It's interest in Iran goes way back to before the first world war, but it was oil, not ports, that drove that."

You can't say that Russia needed oil, that's like saying it needed farmland.
The Soviets had Iraq and Turkmenistan. Assuming they were interested in getting Iran, having Afghanistan would a step in that road. Of course, if they could get Turkey, that would better than Iran or anything else.
But you are familar with chess. The Russians also liked the sport.
This was all about defeating the West.

"Besides, before long, Russia will have all the year-round, ice-free ports it needs: on the Arctic Ocean."

I wouldn't count on it. It was more probably that would have been the case in the 1930's as it is today. And more closer to a reality 1000 year ago, than today. It's possible the arctic could become mostly ice clear during the summer- that hasn't happened yet. And if it did then one of course would still have seasonal variation which make transportation possible near the summer months on some year and it would possibly have less time available in next year or next 5 years. But unless you change the tilt of the earth axis, you are still going to have winter being mostly dark and very cold- and ice will form.

Of course the Russia are somewhat interested in reflecting light from space to at least provide light in the arctic regions. If the Russian were better at Capitalism this could possible be within 50 years or so. But another problem with idea of "year-round, ice-free ports" if you hindering the development business, this doesn't do you much good.

In summary the Soviets didn't want a warm water port for commerce purposes, but rather to disrupt commerce dependent on shipping.