Its the usual android tv behavior as it shows such controls on all compatible devices. For me it only shows on most of the cellphones but not on any of my windows laptops/desktop!
But its reverse for my desktop as it shows my desktop name in TVs devices menu for casting though I never tried.
You have already tried Turn off cast media controls guess something needs to be done from your devices settings.
Try to enter TVs google casting settings if it shows anything. Also, try to disable BT on all your devices.
family members have their own accounts logged in yet it shows, even shows without signing in to google chrome just the device has to be connected to same wifi network
This has got nothing to do with a specific account as its a device specific feature.
One important catch is I dont use chrome browser at all on any of my laptops/desktops and even if I have to, I haven't logged into my google account in any chrome browsers! I keep Google account only limited to my android devices--Phones and TVs! Thus, its likely that you have logged in to/use chrome on your laptops and hence the nagging thing!
Try removing the account altogether and check and I think that should solve it else for a common Wifi things it might show irrespective of account logins across devices.
Too much to try and fiddle with but thats how it is! Let us know which experiment works!