I had to try and solve a problem where the Homepod Mini required a password to use AirPlay. On investigation it became clear that it wasn’t possible to use the Home app on my iphone to change it. So I thought it best to take the HomepOd Mini back to my home and work on it in the morning which I did.
After some research it wasn’t clear how you set it up. But I did find how to reset the device which involves holding down a press on the top of the device in the centre. This gives a factory reset and then releases the Homepod to be re-initalised with your iPhone or IPad device.
The Homepod mini now plays from the iPhone or IPad and appears to work as it should without passwords.
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