On the question: 'What does "spend more time" mean here?', from a theoretical vantage, why explore approximations that are based on the time-independent Schrödinger equation?
Perhaps instead, this could be viewed as an application of the nonrelativistic version of the time-dependent Schrödinger equation for the wave function in position space of a single particle (a shared electron) subject to a potential (from an electric field from the respective cases of the chlorine and fluorine atoms).
Conceivably (for those more of an expert in this field), the product could be a theoretically based graphic depiction of the expected position over time. Visually, does the shared pair of electrons spend more time nearer the chlorine atom with HCl? In the case of the HF molecule, does the shared electrons spend more time nearer the fluorine atom?
As an example of one of the more readable discussions on the time-dependent Schrödinger equation in a position basis, complete with graphs, please see, for example,this source. Here is a good educational video describing the probabilistic nature of the quantum realm at here and also this. A related video is found here.