Why it's not wireless anymore?
It only powers on if it's plugged in to the charger. It use be a rechargeable device.
After doing some research I can conclude the following,
According to few forums and google support, the Home Mini does not have a integrated battery and only works using the 5V 1.8A adapter.
None of the Google Home products feature this anyway (Which does make me wonder why you'd think it was rechargeable before)
So basically, sorry but no it does not have a rechargeable battery.
HOWEVER, the Google Home (standart, not mini) has an option to get a "portable battery base", which gives 8 hours of use (Info found here: https://www.cnet.com/news/add-a-portable... )