ATTiny would definitely work. Ive use them for really really long timer systems with some trial and error.
You should maybe just look at a bigger battery depending on what lifetime you would expect? They are not exactly super low power(at least the ones I have used)
Just log into your routers admin panel and see if there are any online devices online that arent yours? That would be my goto because then you can just block them from the panel?
otherwise via linux cli you can do arp-scan and youll see online devices in your subnet. Theres also a few options to scan different interfaces