Add UserId newtype and WebSocket ping keep-alive

Replace raw String user IDs with a UserId newtype in domain for
type safety, and add 30s ping/pong to prevent idle WebSocket
disconnects.

crates/application/tests/place_pixel.rs

@@ -1,14 +1,18 @@
 mod common;
 
 use application::canvas::place_pixel::{Command, Outcome};
-use domain::{BroadcastEvent, Color, Position};
+use domain::{BroadcastEvent, Color, Position, UserId};
+
+fn uid(id: &str) -> UserId {
+    UserId::new(id.to_string())
+}
 
 macro_rules! place {
     ($state:expr, $user:expr, $x:expr, $y:expr, $color:expr) => {
         application::canvas::place_pixel::execute(
             &$state,
             Command {
-                user_id: $user,
+                user_id: &uid($user),
                 position: Position::new($x, $y),
                 color: Color::new($color),
             },

crates/application/tests/snapshots.rs

@@ -3,7 +3,7 @@ mod common;
 use std::sync::Arc;
 
 use application::AppState;
-use domain::Color;
+use domain::{Color, UserId};
 
 fn state_with_persistence(persistence: common::FakePersistence) -> Arc<AppState> {
     let spy = common::SpyBroadcaster::new();
@@ -22,10 +22,11 @@ fn save_snapshot_persists_current_canvas() {
     let saved_ref = persistence.saved_ref();
     let state = state_with_persistence(persistence);
 
+    let user = UserId::new("user".to_string());
     application::canvas::place_pixel::execute(
         &state,
         application::canvas::place_pixel::Command {
-            user_id: "user",
+            user_id: &user,
             position: domain::Position::new(0, 0),
             color: Color::new(0xFF),
         },

crates/application/tests/soldiers.rs

@@ -1,40 +1,41 @@
 mod common;
 
-use domain::BroadcastEvent;
+use domain::{BroadcastEvent, UserId};
+
+fn uid(id: &str) -> UserId {
+    UserId::new(id.to_string())
+}
 
 #[test]
 fn connect_increments_count() {
     let (state, _) = common::test_state();
-    assert_eq!(
-        application::soldiers::connect::execute(&state, "a".into()),
-        1
-    );
-    assert_eq!(
-        application::soldiers::connect::execute(&state, "b".into()),
-        2
-    );
-    assert_eq!(
-        application::soldiers::connect::execute(&state, "c".into()),
-        3
-    );
+    assert_eq!(application::soldiers::connect::execute(&state, uid("a")), 1);
+    assert_eq!(application::soldiers::connect::execute(&state, uid("b")), 2);
+    assert_eq!(application::soldiers::connect::execute(&state, uid("c")), 3);
 }
 
 #[test]
 fn disconnect_decrements_count() {
     let (state, _) = common::test_state();
-    application::soldiers::connect::execute(&state, "a".into());
-    application::soldiers::connect::execute(&state, "b".into());
+    application::soldiers::connect::execute(&state, uid("a"));
+    application::soldiers::connect::execute(&state, uid("b"));
 
-    assert_eq!(application::soldiers::disconnect::execute(&state, "a"), 1);
-    assert_eq!(application::soldiers::disconnect::execute(&state, "b"), 0);
+    assert_eq!(
+        application::soldiers::disconnect::execute(&state, &uid("a")),
+        1
+    );
+    assert_eq!(
+        application::soldiers::disconnect::execute(&state, &uid("b")),
+        0
+    );
 }
 
 #[test]
 fn disconnect_unknown_user_is_harmless() {
     let (state, _) = common::test_state();
-    application::soldiers::connect::execute(&state, "a".into());
+    application::soldiers::connect::execute(&state, uid("a"));
     assert_eq!(
-        application::soldiers::disconnect::execute(&state, "unknown"),
+        application::soldiers::disconnect::execute(&state, &uid("unknown")),
         1
     );
 }
@@ -42,7 +43,7 @@ fn disconnect_unknown_user_is_harmless() {
 #[test]
 fn connect_publishes_soldier_count() {
     let (state, spy) = common::test_state();
-    application::soldiers::connect::execute(&state, "a".into());
+    application::soldiers::connect::execute(&state, uid("a"));
 
     let events = spy.events();
     assert_eq!(events.len(), 1);
@@ -52,8 +53,8 @@ fn connect_publishes_soldier_count() {
 #[test]
 fn disconnect_publishes_soldier_count() {
     let (state, spy) = common::test_state();
-    application::soldiers::connect::execute(&state, "a".into());
-    application::soldiers::disconnect::execute(&state, "a");
+    application::soldiers::connect::execute(&state, uid("a"));
+    application::soldiers::disconnect::execute(&state, &uid("a"));
 
     let events = spy.events();
     assert_eq!(events.len(), 2);
@@ -63,26 +64,27 @@ fn disconnect_publishes_soldier_count() {
 #[test]
 fn disconnect_clears_cooldown() {
     let (state, _) = common::test_state();
-    application::soldiers::connect::execute(&state, "user-1".into());
+    let user = uid("user-1");
+    application::soldiers::connect::execute(&state, user.clone());
 
     application::canvas::place_pixel::execute(
         &state,
         application::canvas::place_pixel::Command {
-            user_id: "user-1",
+            user_id: &user,
             position: domain::Position::new(0, 0),
             color: domain::Color::new(0xFF),
         },
     )
     .unwrap();
 
-    application::soldiers::disconnect::execute(&state, "user-1");
+    application::soldiers::disconnect::execute(&state, &user);
 
     // Reconnect with same ID — cooldown should be gone
-    application::soldiers::connect::execute(&state, "user-1".into());
+    application::soldiers::connect::execute(&state, user.clone());
     let result = application::canvas::place_pixel::execute(
         &state,
         application::canvas::place_pixel::Command {
-            user_id: "user-1",
+            user_id: &user,
             position: domain::Position::new(1, 1),
             color: domain::Color::new(0xAA),
         },