feat(FN-4401): complete remaining auto-claim snapshot integration

Fusion-Task-Id: FN-4401
Fusion-Task-Lineage: c1b6c497-b22c-48d5-b1c8-299877bf09ac

packages/core/src/__tests__/settings-parity.test.ts

@@ -83,6 +83,20 @@ describe("settings key parity", () => {
     expect(DEFAULT_PROJECT_SETTINGS.heartbeatMultiplier).toBe(1);
   });
 
+  it("defaults autoClaimCandidatesInPrompt to 5 and keeps it project-scoped", () => {
+    expect(DEFAULT_PROJECT_SETTINGS.autoClaimCandidatesInPrompt).toBe(5);
+    expect(isProjectSettingsKey("autoClaimCandidatesInPrompt")).toBe(true);
+    expect(isGlobalSettingsKey("autoClaimCandidatesInPrompt")).toBe(false);
+  });
+
+  it("documents autoClaimCandidatesInPrompt expected integer range", () => {
+    const inRange = [0, 1, 5, 10];
+    const outOfRange = [-1, 11, 100];
+
+    expect(inRange.every((value) => Number.isInteger(value) && value >= 0 && value <= 10)).toBe(true);
+    expect(outOfRange.every((value) => Number.isInteger(value) && value >= 0 && value <= 10)).toBe(false);
+  });
+
   it("defaults sibling branch rename escape hatch to disabled", () => {
     expect(DEFAULT_PROJECT_SETTINGS.executorAllowSiblingBranchRename).toBe(false);
     expect(isProjectSettingsKey("executorAllowSiblingBranchRename")).toBe(true);

packages/core/src/settings-schema.ts

@@ -171,6 +171,7 @@ export const DEFAULT_PROJECT_SETTINGS = {
   maxWorktrees: 4,
   pollIntervalMs: 15000,
   heartbeatMultiplier: 1,
+  autoClaimCandidatesInPrompt: 5,
   groupOverlappingFiles: true,
   overlapIgnorePaths: [],
   autoMerge: true,

packages/core/src/types.ts

@@ -2093,6 +2093,8 @@ export interface ProjectSettings {
    *  For example, 0.5 halves the interval (faster checks), 2.0 doubles it (slower checks).
    *  Must be > 0. Default: 1 (no change). */
   heartbeatMultiplier?: number;
+  /** Number of auto-claim candidates rendered in no-task heartbeat prompts. Range: 0-10. Default: 5. */
+  autoClaimCandidatesInPrompt?: number;
   groupOverlappingFiles: boolean;
   /** File/directory paths to ignore when evaluating overlap serialization.
    *  Entries are project-relative paths (for example: `docs/README.md`, `docs/`, `generated/*`).