Humble Bundle is a shop that is based around offering external keys. Mostly Steam keys. You can not download a Humble version of the game.
I now get what you mean with advertisement. Thanks for clearing up that this is shown before. Itch needs to rework this system completely. If we consider "false advertisement", even the text "Buy 1439 games" falls under this.
Also, I am not even sure if they can "advertise" any Steam keys at all, as they are optional and not covered by their tos. At the very least they need to include disclaimers about how those are extra, are not guaranteed, can run out of stock and so on. Even on the game pages that do offer them for regular purchases.
https://itch.io/docs/legal/terms#4-publisher-content
a non-exclusive, perpetual license to access the content and to use, reproduce, distribute, display and perform such content as permitted through the functionality of the Service. Users shall retain a license to this content even after the content is removed from the Service.
The above text is what you actually buy, when you pay for a project. There is no mention of any external keys. It is a license for the content on the project page. An external key is a digital thing, not a license. After application, you also own the content on a different platform, under different terms of service. It's not even tied to the buyer, it's just a key, that could end up on a key reseller shop.
Itch unfortunately uses imprecise wording at a lot of places. But I think this wording here is intentional:
If your project is being sold on other marketplaces, such as Steam, you can give away external keys to people who own your project
But their "advertisement" is not reflecting this properly. Sure, they have hints in their faq, that big bundles and charity bundles are not supposed to include external keys, due to ... reasons, but ... reasons do not matter for anything that might fall under advertisement laws.
but they also have to honor what is promise
From a practical viewpoint. "they" would have to be the developers manually adding the keys and as far as I know, they could remove the Steam key feature from their page at any moment without giving a reason. If you buy a game that currently has a Steam key, and do not claim that key, and the feature gets removed from the game, you cannot demand the external key later, because you did not buy a key, you bought a license to the projects's files.
Unlike with those Humble Bundle pages, where you actually do buy the Steam keys.