Implement Homeworld mechanics through Caladan reinforcement checkpoint

Connect typed Homeworld custody, transport, battle, income, revival and Caladan reinforcement flows with private multiplayer recovery and controls. Preserve the optimized test workflow and keep unfinished rules modes gated. Verified with 3682 offline tests, typecheck, lint, production build and 40 HTTP tests; existing saved games remain unchanged.

game/homeworld-population.ts

@@ -0,0 +1,56 @@
+import { HOMEWORLD_CARDS, type HomeworldId } from './homeworld-cards';
+import {
+  homeworldForceGroups,
+  type HomeworldCustody,
+  type HomeworldCustodyContext,
+} from './homeworld-custody';
+
+export type HomeworldPopulation = {
+  location: string;
+  card: HomeworldId;
+  native: string;
+  population: number;
+  side: 'high' | 'low';
+  nativeBattleStrength: number;
+  /** Printed potential, not an award or proof of occupation eligibility. */
+  printedOccupiedSpice: number;
+  /** Added only when the native faction is otherwise taking the named benefit. */
+  extraFreeRevival: number;
+  extraCharity: number;
+};
+
+/** Public physical projection only. Occupier entitlements and effect timing are
+ * separate: occupation can retain a low penalty after native population rises.
+ * No player advantage, income, battle result or game action is applied here. */
+export function homeworldPopulations(
+  context: HomeworldCustodyContext,
+  custody: HomeworldCustody,
+): HomeworldPopulation[] {
+  return homeworldForceGroups(context, custody).map((home) => {
+    const faction = context.players.find((p) => p.id === home.native)!.faction;
+    const card = HOMEWORLD_CARDS.find((candidate) =>
+      home.secondary
+        ? candidate.id === 'salusa_secundus'
+        : candidate.faction === faction && candidate.id !== 'salusa_secundus',
+    )!;
+    const native = home.forces[home.native];
+    const population =
+      card.reserveType === 'sardaukar'
+        ? native.elite
+        : native.normal + native.elite;
+    // Global minimum-high rule resolves Salusa's overlapping printed endpoints.
+    const side = population >= card.high.reserves.min ? 'high' : 'low';
+    const bonus = side === 'low' && card.id !== 'salusa_secundus' ? 1 : 0;
+    return {
+      location: home.id,
+      card: card.id,
+      native: home.native,
+      population,
+      side,
+      nativeBattleStrength: card[side].battleStrength,
+      printedOccupiedSpice: card.occupied.spiceIcons,
+      extraFreeRevival: bonus,
+      extraCharity: bonus,
+    };
+  });
+}