>> if you insist on unreasonable enough standard of evidence

One single plausible scenario is not an unreasonable thing to ask for - just one.

If a politician/celebrity/tech person with significant influence/power claims that something might end humanity then they absolutely have the utterly minimal standard of evidence which is to describe one single realistic plausible mechanism at a detailed level that might lead to the worst possible thing ever to happen.

I expect they are not to your very high standards of "non-handwavey, detail exactly how it happens", but this paper from Andrew Critch and Jacob Tsimerman describes 5 different scenarios where catastrophic human casualties occur as a result of AI either being misused or going out of control: https://arxiv.org/pdf/2507.09369

I find the scenarios quite plausible, especially section (3a), which examines the consequences of a global war involving mostly autonomous drone militaries (which is a reality many states appear to be heading towards, following on lessons from the Ukraine war).