I personally find standardization difficult to wrap my brain around if I want to interpret the coefficients. What does a 1 standard deviation change in the binary spring variable actually correspond to? Could I even explain it my grandpa over a beer? I find these sorts of transformations more useful in settings where I am, or my audience is, less familiar with the baseline. For example, a one standard deviation increase in the number of murders conveys the seriousness of the situation very well.
I would advise you to search for the key words "logit" and "marginal effects" on this site. For example, the formulas can be found here. You will still have to decide on the right units to use for such comparisons for the continuous variables, but these formulas should help you proceed from there.
I am not sure what your field is, but imagine trying to describe effect of seasons and temperature on the probability that a person buys an ice cream using a logit model. I think it is still meaningful to compare the expected increase in the probability of a sale during summer (relative to winter baseline or even relative to spring) to the effect of 10 degree temperature rise, particularly if you model includes interactions between them. You can even compare the effect of a 10 degree change in summer versus 10 degree change in winter. You can even get fancier and look at how the effect of a 10 degree temperature rise on the probability varies with a marketing campaign in winter versus summer. You can even back out how much the temperature has to drop on Saturday to get the same reduction as the seasonal change from Saturday to Monday. I find these sorts of comparisons perfectly natural and interesting.