refactor(application): extract vacation management into application use-cases

Moves approve, reject, cancel, and request vacation business logic
out of the tRPC procedure layer into packages/application, matching
the pattern used by allocation use-cases.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

packages/api/src/__tests__/assistant-tools-vacation-review-cancel.test.ts

@@ -72,13 +72,13 @@ describe("assistant vacation mutation tools", () => {
         message: "Rejected vacation for Alice Example: Capacity freeze",
       }),
     );
-    expect(db.vacation.updateMany).toHaveBeenCalledWith(
+    expect(db.vacation.update).toHaveBeenCalledWith(
       expect.objectContaining({
         where: expect.objectContaining({ id: "vac_cancelled" }),
         data: expect.objectContaining({ status: "APPROVED" }),
       }),
     );
-    expect(db.vacation.updateMany).toHaveBeenCalledWith(
+    expect(db.vacation.update).toHaveBeenCalledWith(
       expect.objectContaining({
         where: expect.objectContaining({ id: "vac_pending" }),
         data: expect.objectContaining({ status: "REJECTED", rejectionReason: "Capacity freeze" }),