I’ve come to like Fast N Fitness: https://f-droid.org/packages/com.easyfitness/

I don’t know the answer to your question. But I recently discovered the PWA addon for firefox, and it can accomplish most of what you are describing with the icons and launchers; however it’s not profiles, it installs certain websites as apps in a new firefox runtime, and only allows one tab open at a time per pwa.