fix(client): clear gateway status from welcome identity

The client initialized gateway connectivity from ServerWelcome, but welcome only
exposed a boolean. If a gateway disconnected before the client saw the catch-up
PeerJoined event, the later unknown PeerLeft could not be tied to the gateway
and the status could stay connected.

Carry an optional gateway peer id in ServerWelcome. The relay fills it from the
joining gateway or the existing room gateway, and the Windows client stores it
so a matching unknown PeerLeft clears gateway connectivity. The boolean remains
for wire compatibility with older welcomes that do not carry the id.

Test Plan:
- cargo fmt --check
- cargo test -p lanparty-ctrl server_welcome
- cargo test -p lanparty-relay accepts_gateway_and_client_into_room
- cargo test -p lanparty-relay reports_missing_gateway_to_client_joining_first
- cargo test -p lanparty-client-win relay_lifecycle
- cargo test -p lanparty-client-win \
  clears_gateway_status_when_welcome_gateway_leaves_before_join_event
- cargo test -p lanparty-relay bridges_real_client_and_gateway_sessions
- cargo test -p lanparty-client-core connects_to_relay_control_stream_as_client
- cargo test --workspace
- cargo clippy --workspace --all-targets -- -D warnings
- cargo build --release -p lanparty-relay -p lanparty-gateway
- git diff --check
- git diff --cached --check

Refs: MVP lifecycle cleanup

README.md

@@ -105,7 +105,8 @@ Public relay binary and relay-owned room state:
 - live Ethernet datagram forwarding with no ingress reflection
 - forwarding drops for Ethernet frames above the negotiated TAP MTU
 - per-peer egress budget checks against the negotiated datagram size
-- reliable `PeerJoined`/`PeerLeft` notifications to existing room peers
+- reliable `PeerJoined`/`PeerLeft` notifications plus gateway identity in
+  welcome messages
 - L2 safety filters for invalid-source, jumbo, switch-control, remote VLAN
   tags, remote IPv6 fragments, IPv4/IPv6 DHCP-server, and IPv6-RA frames,
   including frames behind ordinary IPv6 extension headers