Thank you @Marek-h for your suggestion. Using NSWorkspace.shared.setIcon(image, forFile: bundle.path, options: []) has the same effect, only works temporarily while the app is opened.

Seems like the reason the icon keeps reverting back is because I'm running a signed app. MacOS's code signing and app sandboxing prevent permanent modifications to the app bundle, which is what I'm trying to do when setting the icon.

Seems like the only way to do this for now will be to distribute the app from outside the App Store.