Changes which way listings flow between this server and one network it belongs to. network_id is the full Network ID and both outbound (your listings appear on the peer servers) and inbound (peer listings appear here) must be given. By default Discord shows the /group-admin commands only to members with Manage Server.
Anything that is not a complete Network ID is refused with That doesn't look like a Network ID. The server must already be in the network; otherwise the reply is Network membership not found with a pointer to /group-admin network join.
The private reply is Visibility updated with the new mode: Full federation, Outbound only, Inbound only, or Disabled when both are off. Turning a direction off retires the Network listing copies that can no longer be reached, peer listings posted here when inbound goes off and your own listings on the peers when outbound goes off: their buttons are removed and they are replaced with This listing is no longer shared with this server. Public listings are left alone.
Disabled keeps the membership but stops sharing both ways, which is different from /group-admin network leave. This command does not check whether Group Finder is switched on for the server.