I'm not an expert on the tech and can't say. Just going on what the Economist article talks about, South Korean manufacturing represents a tiny fraction of the smallest processes right now. The article you linked says the 3nm will start producing in 2024. That's good news, maybe there's competition coming.
The Samnsung 3nm will be sold in 2024, produced in 2023. I'll admit TSMC might have an edge in the timing but the OP article also hedges their statements by specifying TSMC will have limited availability of the 3nm in the second half of 2023 and the Apple product refresh in Fall 2023 might contain these 3nm components.
I just don't think Samsung is really that far behind as right now both companies are just selling promises.
Samsung's 4nm was substantially less advanced than TSMC's 4nm (compare Qualcomm's Snapdragon 8 Gen 1 to 8+ Gen 1 when they switched to TSMC). The same is plausible for 3 nm.