Adb backup exists, though I haven't tried it, and Google cloud backup does this. However, if you trust Google, you probably already trust the US.
Unfortunately, I don't know of any other app that does this on an unrooted phone.
>Adb backup exists, though I haven't tried it,
It's very patchy, and many (most?) apps opt out, so it's functionally useless.
Google cloud backup has never done this for me. It seems like it'll restore a whole lot of stuff, but details like getting my Nova Launcher screen back (version pinned to before it was sold - alternatives just aren't good enough yet) or a bunch of the little logins and details has never done it for me.