FN-5823: add shared-branch-group entry-point verification coverage

Add end-to-end checks to keep branch entry points aligned with shared-branch-group flow.

- add dashboard integration tests covering shared-branch-group entry behavior across entry points
- update TaskCard branch-group chip rendering to match shared assignment metadata handling
- extend mission store test/docs coverage for shared-branch-group alignment expectations

Files changed:
 docs/missions.md                                   |  10 +
 packages/core/src/__tests__/mission-store.test.ts  |   4 +
 packages/dashboard/app/components/TaskCard.tsx     |  22 +-
 packages/dashboard/src/__tests__/shared-branch-group-entry-points.test.ts       | 354 +++++++++++++++++++++
 4 files changed, 381 insertions(+), 9 deletions(-)

Fusion-Task-Id: FN-5823

Fusion-Task-Lineage: 7c06e2d2-0233-4a02-a79e-daecab47f0a9

packages/core/src/__tests__/mission-store.test.ts

@@ -2435,6 +2435,10 @@ describe("MissionStore", () => {
       expect(firstTask?.branch).not.toBe(secondTask?.branch);
       expect(firstTask?.branchContext?.groupId).toBe(`mission:${mission.id}`);
       expect(secondTask?.branchContext?.groupId).toBe(`mission:${mission.id}`);
+      expect(firstTask?.branchContext?.assignmentMode).toBe("shared");
+      expect(secondTask?.branchContext?.assignmentMode).toBe("shared");
+      expect(firstTask?.branchContext?.source).toBe("mission");
+      expect(secondTask?.branchContext?.source).toBe("mission");
 
       const branchGroup = ts.getBranchGroupBySource("mission", mission.id);
       expect(branchGroup?.branchName).toBe("feature/shared");