The value of optionality is defined by drawing out the decision tree for the scenarios with and without the option, doing backwards induction for the optimal strategy and estimating the value of each. (In financial option theory, you calculate the price of a literal option by simulating out all of the possible price trajectories and how you would respond to them, to figure out what would be a too cheap or too expensive price.) Because scenarios can be arbitrarily complex, no general answer is possible. If an option wouldn't be used at any state of the world, it might have a value of $0, for example, and this is automatically taken into account: the backwards induction will produce a policy that never invokes the option, and the difference in the value of the 2 scenarios = $0 option value.

For the house scenario, you would, say, define scenarios where each month you can sell/rent/live-in-it and there are random shocks (like Airbnb prices going up/down or housing prices going up/down, I guess), and a horizon of like 10 years and then do backwards induction to understand the value of being able to exploit decreases in Airbnb prices or to shelter in your house from Airbnb price surges.

Well, I’d probably start with some expected value stuff. What's the probability of a scenario, multiplied by the payoff. For housing specifically, I know the govt does a weird calculation for inflation in housing where they ask honeowners what they think they could rent their house for, something like that may help you make a framework for directly comparing