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I’m pretty sure you can just buy a light bulb mount for your home mini, it screws in to an empty socket to provide power. Probably something like this: [link]
Not OP but check out Dock Socket. Haven't used one because I don't have recessed lighting but it does just this.
[link] ... If you don't need light there.
Here are some ways to mount a Google home on the wall or celing. There are many more just look on Amazon:
Dock Socket: Light Socket Mount for Google Home Mini [link]
The Simple Built-in Google Home Mini Mount: Custom Built-in Wall or Ceiling Mount Holder for Home Mini Voice Assistants by Google - Designed in The USA by Mount Genie (1-Pack) [link]
360 Electrical 360579 PowerClip Outlet Mount for Google Home Mini - Google Plug-in Bracket Stand Holder Case, for Kitchen, Bathroom, Bedroom, Living Room, Office, Charcoal [link]