I doubt this very much. Surely the vast majority of running code is some chunk of Chrome, Android, or the JVM ("billions of devices run Java...") or something. All those things were produced by software engineers with more than surface-level understanding.
But there is certainly more codebases out there running some python or js written by designers, data analysts etc then those produced and curated by software engineers.
Let's be honest: web browsers are really bad. Overly complicated machines made to print images and text on the screen. The web got sideways long ago, first because it was cool to add crap in websites, then because it made profit and allowed monopolies to make more profit by moving everything to damn webapps. And finally it allows companies to screw users by renting software on the damn cloud.
And they profit by making it as accessible as possible, such that everyone and their dog can produce a crappy webapp that will show their ads or track their users.
Webtech is part of what makes software really bad, even if it was created by good engineers. Because people don't want quality: they want cheap new crap.