Method selection - multivariable non-parametric I am not sure about the method selection for my data.
Dependent variable: Continuous variable and grouped in ordered categories. As continuous it is not normally distributed but skewed to the right. As categories, they are similar in size in the number of observations except for baseline which is defined based on clinical cut-off.
Explanatory variable: Continuous variable grouped as binary based on clinical cut-off. As continuous it is normally distributed.
Potential risk factors looking into: 2 binary, 1 with three non ordered categories
I looked at potentially using ordered logistic regression, but are now considering a non-parametric method. Was recommended to use the Whitney U test, but not sure what method I can use for multivariate analysis. Considering non-parametric series regression.
What method and test would you use?

This is a multivariable problem, not a multivariate (multiple dependent variable) problem.
If you were to analyze the binned data a semiparametric ordinal regression model such as the proportional odds model would be the logical choice.  But do not analyze the binned data.  The physician has made a terrible mistake in discarding valuable information in the data by the use of arbitrary binning.  It may be worth spending some time demonstrating the information loss, e.g., by comparing the likelihood ratio $\chi^2$ statistic for the whole model with and without binning, using the proportional odds model for both.  (Yes the PO model works great for continuous Y just as its special case the Wilcoxon test does).  An introduction to the PO model may be found in the Nonparametrics chapter of BBR.
To the bigger question, the role of a statistician is to give the collaborator what she needs, not what she wants.  Collaboration is optimal when each collaborator uses their own expertise and there is a logical division of labor.  It is a bad idea to be a spectator to bad analytical practice.  There is an ethical obligation to not use methods known to be inferior. See https://www.fharrell.com/post/principles.
If you are in a setting where your expertise is not respected it is sometimes best to find a new setting or a new collaborator in an existing place of employment.  Good statisticians/data scientists can find jobs almost anywhere nowadays.  Sometimes we have to capitalize on this "buyer's market" in order to be in an environment for optimal growth as an analyst.
For information about binning and information loss see https://www.fharrell.com/post/ordinal-info.  Another way to demonstrate information loss is to show that a predictor predicts variation of Y even within one of the forced intervals.
