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

docs/missions.md

@@ -47,6 +47,16 @@ Supported modes:
 
 The Mission Manager create/edit form exposes this as **Branch strategy** plus a conditional **Branch name** field for `existing` and `custom-new`.
 
+### Shared branch-group invariant across entry points
+
+Across all branch entry points (planning/subtask creation, mission triage, and New Task `shared-group` creation), Fusion enforces one rule:
+
+- Persist a **per-task working branch** on each task (the checkout branch used for execution).
+- Persist the shared branch only as the **group merge target** via `branchContext.groupId` → `branch_groups.branchName`.
+- Never persist the shared branch itself as a task working/checkout branch.
+
+This keeps member execution isolated per task while still routing member landings into a single shared integration branch.
+
 ### Dashboard
 
 Use the Mission Manager UI to create missions and build hierarchy interactively.