Between other profiles, not main
How do you transfer apps between profiles?
You can't. Only Owner can transfer to secondary profiles.
Resurr I usually just install the apps in the other profile via the same "app store" or I download them directly via Vanadium. If it's an app that I can only get via Google Play, I have used Aurora to download the apk, put the apk on an external drive, and move the apk to the other profile. It all depends on what I want to use the other profile for or how lazy I want to be with setting it up.
Resurr This is a common problem with Aurora. The accounts they use are shared and are rate limited by Google. Google could ban all of Aurora's accounts pretty easily if they ever chose to do so.
I also think that I should note that Aurora isn't as secure as Google Play. They don't do the same checks as Google Play. If possible, I'd suggest you install apps via Google Play. I usually avoid Aurora, but have used it in the past when I was being lazy and when I was installing an app that was already installed in another profile (so I know the signatures match).
Oggyo It's been a long time since I've done this and I'm not sure if it works with the most recent version of Aurora, but I just started the install in Aurora, then I don't install after the download completes. Then, I find the apk, which is stored somewhere. I tried to do it just now, but Aurora isn't working for me. I don't know where they're saved, but it's something like ~/Aurora/Store/ or ~/Android/data/com.aurora.store/files/Downloads/com.aurora.store/.