There are people confidently claiming they can’t and then other people expressing skepticism at their confidence and/or trying to get them to nail down what they mean.

... someone else points out that the same models that can't "think" are somehow turning in gold-level performance at international math and programming competitions, making Fields Medalists sit up and take notice, winning art competitions, composing music indistinguishable from human output, and making entire subreddits fail the Turing test.

Uh huh. Good luck getting Stockfish to do your math homework while Leela works on your next waifu.

LLMs play chess poorly. Chess engines do nothing else at all. That's kind of a big difference, wouldn't you say?

To their utility.

Not sure if it matters on the question "thinking?"; even if for the debaters "thinking" requires consciousness/qualia (and that varies), there's nothing more than guesses as to where that emerges from.

For my original earlier reply, the main subtext would be: "Your complaint is ridiculously biased."

For the later reply about chess, perhaps: "You're asserting that tricking, amazing, or beating a human is a reliable sign of human-like intelligence. We already know that is untrue from decades of past experience."

I don't know who's asserting that (other than Alan Turing, I guess); certainly not me. Humans are, if anything, easier to fool than our current crude AI models are. Heck, ELIZA was enough to fool non-specialist humans.

In any case, nobody was "tricked" at the IMO. What happened there required legitimate reasoning abilities. The burden of proof falls decisively on those who assert otherwise.

This is exactly the problem. Claims about AI are unfalsifiable, thus your various non-sequiturs about AI 'thinking'.