feat(ui): screen-level history for the app-shell (Back → lobby)

Mirror the screen into browser history via SvelteKit shallow routing
(pushState/replaceState with page.state) so Back/Forward move between
screens while the URL stays at /game/. Overlays (game, lobby-create) push;
lobby/login replace. A popstate→page.state effect syncs the store back
without re-pushing (no loop); the boot stamp puts a restored overlay above
the load entry so Back falls through to lobby. In-game view switches never
touch history.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

ui/frontend/src/lib/app-nav.svelte.ts

@@ -20,6 +20,8 @@
 // in the shell via SvelteKit shallow routing; this module is the source of
 // truth, history only mirrors it.
 
+import { pushState, replaceState } from "$app/navigation";
+
 export type AppScreen = "login" | "lobby" | "lobby-create" | "game";
 
 export type GameView =
@@ -158,6 +160,34 @@ class AppScreenStore {
 			this.#gameId = null;
 		}
 		persist();
+		this.#syncHistory();
+	}
+
+	/**
+	 * syncFromHistory applies a screen restored from browser history (a
+	 * Back/Forward popstate) WITHOUT pushing a new entry. An absent/unknown
+	 * screen (the load entry beneath an overlay) falls back to lobby.
+	 */
+	syncFromHistory(screen: AppScreen | undefined, gameId: string | null): void {
+		const next =
+			screen !== undefined && APP_SCREENS.includes(screen) ? screen : "lobby";
+		this.#screen = next;
+		this.#gameId = next === "game" ? gameId : null;
+		persist();
+	}
+
+	// Mirror the screen into browser history via shallow routing (the URL is
+	// unchanged — the address bar stays at /game/). Overlays (game,
+	// lobby-create) push a new entry so browser Back returns to the lobby
+	// beneath; lobby/login replace in place.
+	#syncHistory(): void {
+		if (typeof window === "undefined") return;
+		const state: App.PageState = { screen: this.#screen, gameId: this.#gameId };
+		if (this.#screen === "game" || this.#screen === "lobby-create") {
+			pushState("", state);
+		} else {
+			replaceState("", state);
+		}
 	}
 }