The people who use the phrase "No evidence" mean "no good evidence that moves the dial to a significant degree". But for brevity they shorten it to "no evidence" and assume people are capable of filling in the gaps instead of interpreting it extremely literally. We often speak without perfect precision in order to communicate ideas quickly and easily, and it's up to the reader to extend charitable and common sense interpretations.

The problem is that when public figures come out and say "there's no evidence...", they aren't assuming the public are smart and capable of understanding nuance and able to fill in gaps.

At least in the COVID context, they were worried that any nuance would confuse the public, so they simply gave the simplified, dumbed down version.

Of course it backfired a bit. I honestly don't know what's the optimal play for them, but it seems a bit revisionist to say that they assumed the public was capable of filling in the gaps...

The one abuse of that phrase I recall was around masks, where policymakers and science communicators initially said there was "no evidence" that they worked at reducing COVID transmission. I agree with your criticism when it comes to this case.

But when policymakers say there's no evidence for ivermectin's ability to treat COVID, I don't fault them because I see their choice of words as being aligned with the truth. Therefore they are accurately communicating science and good policy.

As with all uses of language, we have to look at it on a case-by-case basis whether it's being weaponized wrongly or used appropriately. I will criticize it when it's used wrongly, and otherwise not criticize it.