Susan, all I could find outside of the Apple smart battery case on Amazon is the Mophie.
Like you, I want the convenience of pressing a button on the case to charge my phone. I had the Mophie case on my iPhone SE and it worked beautifully. I could listen to music while I had the Mophie case on by putting an extender on my headphone jack so I could plug it into my phone.
Since the iPhone 8 no longer has a headphone jack, the charging port is the only one available and I have an adapter for my headphones as I am not ready to buy wireless headphones. The Mophie case blocks the charging port and there is no extender on the market making it impossible for me to listen to music with my headphones while the Mophie battery case is on the iPhone 8. So I don’t think it’s of interest to me while I don’t have wireless earphones.
I have done some research on apple’s smart battery case. Like you said, what it does is drain the case’s battery first even if my iPhone 8 is fully charged. Then once the case is drained, then the iPhone battery is used. The explanation I read is that the iPhone battery won’t be used as much and will last longer because the case battery is used first. For me, I wanted the battery case as protection for the phone in case I drop it and also as a back up battery. Apple has it the other way around in terms of which battery drains first. To me, it looks like Apple wants the battery case to keep draining again and again so it will run out of cycles and people will need to buy another battery case.
I do have a lightweight Anker tiny cylindrical portable charger whose length is my index finger. Maybe I will carry that in my purse as back up in the meantime.
Whenever you start your research, please let me know how it goes. Thanks.