The relay welcome now carries the gateway peer id, but the first Windows client
startup line still only showed whether a gateway was connected. Surface the peer
id there when it is known so manual MVP testers can record it even before or
without relying on a later lifecycle catch-up line.
Keep the older yes/no text when a gateway is connected but the peer id is not
available, which preserves useful output for older welcome payloads.
Test Plan:
- cargo fmt --check
- cargo test -p lanparty-client-win gateway_status
- cargo clippy -p lanparty-client-win --all-targets -- -D warnings
- git diff --check
- git diff --cached --check
Refs: MVP manual validation
ddidderr
edcd30f6bc