Part of the MC LAN Proxy help pages
Read this before you use it. Switch mode is experimental. To work, the app signs in to a Microsoft account and behaves like the Minecraft client. Microsoft has not approved that, and accounts have been banned for it. A ban can affect the whole Microsoft account, not just Minecraft. Use a spare account, never your main one.
On Xbox and PlayStation, MC LAN Proxy makes a server appear in the LAN list. A Nintendo Switch does not join servers that way, so there is nothing for the normal method to answer. The Switch also cannot add a Bedrock server address by itself.
In Switch mode the app publishes your server to Xbox Live as a friend's world. It then appears on the Switch under Play → Worlds or Play → Friends, and you join it from there. The phone stays in the data path and relays the game to the real server, so the Switch must be on the same Wi-Fi as the phone.
If the world is not there, send that account a friend request from the Switch and wait about half a minute.
It is free in both versions of the app. It is not limited to the Switch: any Bedrock device can use it.
Switch mode has been tested on a Bedrock client on Windows, which found the published world, joined it and played through the relay. We have not yet confirmed it on a Switch itself. We would rather say so than guess. If you try it, tell us what you see through the app's Google Play page.
No. A Realm is Microsoft's own hosting. This puts a server you already have an address for in front of a Switch.
We cannot say. Microsoft has not approved this approach, and accounts have been banned for it, so treat the risk as real and use an account you can afford to lose.
LAN discovery changes in 26.60; see Minecraft 26.60: LAN game not showing. Switch mode does not use LAN discovery.