feat(client): report relay route before TAP activation

Use the new route snapshot helper in the Windows client startup path before the
TAP adapter is opened and marked connected. The client now reports the current
relay destination route: selected source address, next hop, interface index,
interface LUID, route prefix, and metric.

This is still diagnostic only. Route pinning remains unwired, and route lookup
failure is a warning so manual TAP frame-pump testing is not blocked by a route
inspection failure. Once mutation is implemented, this snapshot gives the code
the pre-TAP interface data it needs to preserve the real internet path.

Verification note: I attempted to check `lanparty-client-win` for
`x86_64-pc-windows-msvc`, but this host still lacks the Windows C headers
needed by `ring`; the build stops at `assert.h` before the binary crate can be
typechecked for Windows.

Test Plan:
- cargo fmt --check
- cargo test --workspace
- cargo clippy --workspace --all-targets -- -D warnings
- cargo check -p lanparty-client-route --target x86_64-pc-windows-msvc
- cargo clippy -p lanparty-client-route --target x86_64-pc-windows-msvc -- -D warnings
- git diff --check

Refs: PLAN.md

README.md

@@ -130,8 +130,9 @@ cargo run -p lanparty-client-win -- \
 The Windows client binary currently connects to the relay as `role = client`
 with a generated locally administered virtual MAC persisted in
 `lanparty-client-identity.json`, completes the control-stream hello/welcome
-handshake, and then bridges Ethernet frames between the relay and the first
-TAP-Windows6 adapter until shutdown. `--virtual-mac` can still override the
-stored identity for manual testing. On Windows it marks the TAP media
-connected and reports the driver MAC/MTU before forwarding frames. Route
-pinning and automatic TAP MAC/MTU configuration are not wired yet.
+handshake, snapshots the current relay route, and then bridges Ethernet frames
+between the relay and the first TAP-Windows6 adapter until shutdown.
+`--virtual-mac` can still override the stored identity for manual testing. On
+Windows it marks the TAP media connected and reports the driver MAC/MTU before
+forwarding frames. Route pinning and automatic TAP MAC/MTU configuration are
+not wired yet.