I don't think you understand what "rent seeking" actually means.
The NIMBY'ism of preventing new housing is the very definition of rent seeking. By legally locking in, the existing owners prevent others from entering the market due to artificially constrained supply. Airbnb doesn't create the demand; they are just a marketplace and one of many.
"Rent seeking (or rent-seeking) is an economic concept that occurs when an entity seeks to gain added wealth without any reciprocal contribution of productivity."
What contribution to productivity do corporations or people who have enough spare cash to buy available land provide to a society?
AirBnB can be just a marketplace, that doesn't mean it isn't damaging to society at large. Excluding the moral aspects of that is an ideology based on capitalism, it doesn't mean it's right.
Believing that the world is dictated by a reductionist model of supply-and-demand is either myopic or ignorant, the world doesn't work like that, that is a model that works well for a diverse set of markets, not all and not at all if you start to include the social aspects into it.
You can't just start building anywhere and anything, that will kill cities, it's a shallow analysis of a broader scope of issues such as: maintaining livable conditions (as defined by the society and culture of that city, not by some metric of "available units per inhabitant"), maintaining harmony of urban planning, maintaining the cityscape, and so on. Devising the master plan for building is exactly the kind of aspect that a simplified worldview of pure supply-and-demand does not take into account, it's simplistic and unempathetic.
Prices will continue to increase if building new units doesn't take place. AirBnB and greedy landlords shouldn't have the power to increase this damage for short-term profits. And worse: doing that in a rent-seeking way, with little to no benefit to the society of that city apart from some tourism money and "digital nomads" income passing by, rent-seeking behaviour is disgusting, it's pure extraction by virtue of you accumulating enough capital to be able to own a piece of land, that's all, there's no productivity increase for society through this form of extractivism.