My father and I have used the LAN connection for years with no issues. We are in the same room using the same internet connection. He uses laptop, I use pc, we both run Windows 10. Each computer can individually run 1.17.1 with no issues, and we can both connect to a 1.17.1 world via Realms. 

When a 1.17.1 world is opened to LAN, it does not appear in the multiplayer window, and if we use direct connect, we quickly receive the connection timeout error. It doesn't matter which of our computers is hosting the world, the results are the same. If we revert to a previous version, LAN works fine (currently we have settled on 1.16.5).

We really enjoy this new update, and we look forward to Caves & Cliffs part 2, but it is a shame that we cannot play this version together. I hope this issue is fixed soon. In the meantime, if anyone has any suggestions or news on a solution, we would greatly appreciate it.