Wait, what? Are they really removing http(s) basic authentication support from Chrome?

The processes that run on your laptop trying to connect your LAN services, would, outside of Lan, resolve the public DNS record and try to connect to the web hosting server. If the port is 80/443, they would indeed establish connection with the public web server, which could log those requests. This is when certificates and encryption comes into play. If your client programs are using TLS and are not buggy, and you have not uploaded your private certificate key to the public web server, they would just error out, and noting will be leaked. Split horizon DNS (what you are doing) is similar to DNS spoofing attack, TLS/SSL/HTTPS defeats such attacks. You secured your server (by not opening ports), but clients need to be secured too.