Is

App_Plugins

still the right place for custom property editors in 12+? Is it recommended, or even mandatory, to place them there?

Throughout the versions you can do more and more in c#, but the view files and js is still expected to be there, and you can still fully define one via a package.manifest in App Plugins. For packages most have moved over to Razor Class Libraries where they can have it copy static files over on build, so the files may not show in app plugins in your solution but will be there in runtime

Thanks. For now, this is a solution-specific property editor. But it will be re-used for future solutions.

Last I checked, it's not mandatory except for the translation XML files which get loaded automatically. Totally possible to use some other folder (or none) when registering the paths for your property editor's HTML/CSS/JS.