It doesn't help you, but other customers in this forum have reported Google Nest devices showing as "offline" for another household member. It seems to be a recurring issue.
On this post, the problem went away after awhile:
On these posts, no resolution is posted; I don't know whether that means the problem just went away or what:
Thank you for bringing up the concern you're experiencing, I would love to look into this further for you. The first troubleshooting step that I'd recommend would be to restart your device. This process should keep all your settings, and reconnect it to the same Wi-Fi network. This is helpful if it ever freezes, has connection problems, or isn't working normally. Thank you, @MplsCustomer for your help.
Just checking in to make sure that you've seen our responses. Please let me know if you have other questions or concerns as I will be locking this in 24 hours if I won't hear back from you again. Feel free to start a new thread and we'll be happy to help.