Cambridge Dictionary defines and ad as: a picture, short film, song, etc. that tries to persuade people to buy a product or service

My short search really didn't bring up any definition that included the need of the product/service owner knowning that the advertising is happening.

And the message very much qualifies as trying to bring people to buy raycast (or at minimum to use it which usually want people to also pay later on).

I don't see the point in arguing about the definition, but I don't think the message was trying to persuade people to buy raycast. What interest would microsoft have in that? Rather, it seems to me like it was trying to tell raycast users that they can use copilot through raycast.

Regardless, even if the dictionary definition of an ad doesn't require that the ad be created intentionally, it's still the case that if you say "ad" everyone will assume you mean something that was intentionally created to sell a product or service. I recommend checking out this classic post about the noncentral fallacy: http://worstargumentintheworld.com

Dictionary definitions are not helpful in this sort of discussion. The exact definition of “ad” is not the point.