A transaction can occur if the price is >= the seller's cost, and <= the value to the buyer. If it's at the minimum, the seller must pass on the tax or not trade, at the maximum (down to the max minus the tax) , the seller can't pass on (all of) the tax and still trade. We observe that landlords make profit, so we are not at the minimum. Are we at the maximum?

I think there are cases where we are in between for significant periods of time. Consider a positive shock to wages. Can landlords put up prices overnight? I don't think so, unless the landlords all co-ordinate to do so, prices will be sticky as there are always some properties in the market, so it's difficult to be the first to increase rent. Unlike a purchase, a landlord who waits for a buyer at the right price is forgoing income during the void. So the market price can be a Schelling Point.

A tax increase, however, happens at the same time to all landlords. All of them would prefer to pass it on, and they know that so they can assume all other landlords will try to pass it on. If the rent is currently below the maximum possible, they will succeed.

How long it takes prices to adjust I don't know. It is an empirical question, but I don't know what data would answer it. But it seems like it took decades for landlords to capture the two-income surplus after it became common for women to have a career.