I would set up your router, turn off ssid broadcast and forget about it. It's doubtful they have the equipment to find an access point that doesn't actively announce itself to the world .
Edit: it means you will have to manually add your wifi network to your devices by typing in the ssid on them but other than that there shouldn't be any issues
It's not great but it's not really world ending. About a year ago someone filed for unemployment in bot my wife's name and my name. Which came as a shock to my employer as I was was still happily at work. I work for a small mom-n-pop store, my wife works at a mega corporation. She caries insurance etc and one of her companies providers had a leak of ssn and other personal information. We both locked our credit and signed up for a protection pin for filing taxes. We reported to the local unemployment office that they were fraudulent claims. I look back and realized we probably should have locked our credit long ago and got tax pins as well, just for the security side of things.
The funny thing is my employer brought it to my attention. My wife's employer didn't even notice and was getting ready to pay the claim even tho she was still working there as the system is all automated in her company. Eventually it came out about the leak and they are providing 5 years of credit monitoring for free.
Since seeing this picture I have disassembled about 50 nine volts looking for this and have found about 3. Some full of coin cells too.
Edit: I should say it was years ago I first saw this picture. I haven't disassembled 50 batteries in the last 2 minutes
That is using messaging for the web through Google Fi. But there is little reason to do that now as Google messages the app itself can be used through messages.google.com. there are several stand alone computer applications that use the portal as well (messages in the windows store, messages or google-messages package in most distros. Dunno about Mac. Either way, instead of fi being the backend, the app connects directly to your PC. You just have to pair your phone using the app directly.
In theory it's pretty safe. In practice it depends on how much of the network you think has been compromised by various governments. If you are downloading some music or a movie or some adult material your fine, the government in general could care less. If you are looking for something truly illegal (CASM etc) then you deserve to be caught anyway, so go ahead.
Maybe it depends on the access point. When I turn it off on my router there are no beacons sent. Unless you specifically probe the ssid it doesn't announce itself. BUT granted when you make a connection the ssid does show up during the handshake. If you were watching at the exact moment of connection then it would be detectable. I suppose they could use a mass deauther device and cause new connections and detect while that is happening but they they would need to triangulate the location of said ap... Again a lot of extra equipment.