Everything you describe is what I've been thru.
1. A new battery is not requiring a registration for this car vintage. I replaced mine with a same kind from dealer 6 yrs ago, no reg needed.
2. Can you hear the starter turning the engine over? Likely not, not a whirl. If your battery is ok and it sounds like it is, the starter is it. Get a Bosch kit from FCP like I did 3 yrs ago, if it fails ever again they replace it for free (and it will fail, it's a shitty little starter like due to packaging issues):
https://www.fcpeuro.com/products/bmw...-kit-sr0492nkt
Forgot: have INPA, it's useless as the car while it has all sorts of things being monitored has no idea when the starter fails. So no codes to be had.