@Clark_Kent You are right that touchless car washes use high pressure but I suspect that the very aggressive chemicals used by touchless is what removes wax. Think ultra high pH or ultra low pH (like acids). This is explained pretty well at
this Tesla Car Wash website that gets into how the touchless car wash works and why the guidance in the manual is kind of confusing.
Hand wash is what the manual says but personally I use one of two soft touch automatic washes near me that are 1) well maintained and use enough neutral soaps, and 2) use a foam element (not a nylon bristle or cloth). Folks who have not seen these elements up close might mistakenly think it's a brush. But it's not.
If you don't want to hassle with handwashing, learn a little about the differences b/w touchless and friction (foam, brush, cloth, whatever).