I bow to your superior Internet search skills.

First: Cheesiness. The article is not "Written by thelancet.com". It is written by a guy with concerns about labels: Günter Kampf. More about him in another comment.

Günter Kampf feels labeling it a pandemic of the unvaccinated might lull some of the vaccinated into thinking they don't have to worry about following the public health guidelines about mask wearing, hand washing, social distancing, and so forth. I wonder how much of a concern that is, and I note that he doesn't state that it is NOT a pandemic of the unvaccinated, just that he thinks the label is bad. He doesn't argue with any of the points made in the papers he cites.

So that's one way of looking at it. On the other hand the unvaccinated are many, many times more likely to be hospitalized than the vaccinated (see the Toronto Star reference below). When the unvaccinated represent a large majority of the people in the hospitals and especially the ICUs but they come from a small minority of the population I think 'pandemic of the unvaccinated is appropriate'. See the Ontario hospitalization data for Dec 9 2021: https://covid-19.ontario.ca/data

Back on August 17 2021 the Toronto Star crunched some numbers and came up with this: "Unvaccinated Ontarians are ending up in Hospital with COVID-19 20 times as often as fully vaccinated individuals and in the last week have been about 70 times more likely to end up in intensive care..." https://www.thestar.com/news/gta/2021/08/16/we-broke-down-the-hospitalization-risk-of-going-unvaccinated-in-ontario-heres-what-the-numbers-say.html

On that day, August 17 2021, there were 348 new cases of covid in Ontario. Today, Dec 9, there are 1290. https://docs.google.com/spreadsheets/d/1E28C0ylUQ0hHgFySFpXtdjX_LkdY5tlhl-nt0SGhCDg/edit#gid=764546978