Yeah that is kind of vague though. I don't really have other stuff on my LAN (https://biggaybunny.tumblr.com/post/166787080920/tech-enthusiasts-everything-in-my-house-is-wired) right now unless you count my phone.
I'm in another thread right now where a guy is running a simple encrypted chat server on his phone under tmux. That is pretty cool and using an old phone is an interesting alternative to a razzleberry pi if you don't mind running Android and don't need much compute or storage.
I think I see, you're suggesting using a local server as sort of a jump box to the internet, with otherwise disconnected clients. I guess that has some attractions, though in practice I use web browsers all the time, with the usual bug-ridden software stack that surrounds such things. If I were doing anything really sensitive I wouldn't use that approach.