Kaplan-Meier-type curves for continuous covariates It's well known the Kaplan-Meier curve is a univariate time-to-event summary plot. If you want to show differences between groups, you can make a KM curve for each group. In addition you can calculate the p value from a log rank test or a Cox model adjusting for that variable categorically. It's understood that the tests do not test for differences in the survival distributions per se, but rather the hazard ratio. So the graph and test are not one-to-one. Nonproportional hazards reduce the power of the test.
Turning attention to continuous covariates, has anyone proposed clever ways to show something like a KM curve for a continuous adjustment variable? At a basic level you can split a variable according to quintiles, possibly with overlapping ranges. But I wonder if more sophisticated methods have been proposed to detect survival differences visually.

What you are describing actually is a frequent problem. The answer from Thomas Lumley is good, but the estimated conditional survival probabilities are not based on the cox model and are therefore not adjusted for possible confounders. I developed the contsurvplot R-package (https://robindenz1.github.io/contsurvplot/) which can be used to create various graphics to visualize the confounder-adjusted effect of continuous variables on a time-to-event outcome. In this answer Converting survival analysis by a continuous variable to categorical so as to find level of most significant difference you can find more information on this method.
