fix(types): flatten tRPC Zod schema types to resolve TS2589 inference depth errors

Cast Zod schemas with .refine()/.superRefine() to z.ZodType<InferredType> at the
procedure level. This short-circuits TypeScript's deep type recursion through
tRPC's middleware chain, eliminating 4 of 5 @ts-expect-error TS2589 suppressions
in web components (VacationModal, ProjectModal, UsersClient, CountriesClient).

Applied same pattern to allocation, timeline, staffing, dashboard, project, and
resource query/mutation procedures to reduce client-side type depth.

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

packages/api/src/router/allocation-conflict-procedures.ts

@@ -1,7 +1,8 @@
 import { validateAvailability } from "@capakraken/engine";
-import {
-  type AllocationConflictCheckResult,
-  type WeekdayAvailability,
+import type {
+  AllocationConflictCheckResult,
+  AllocationStatus,
+  WeekdayAvailability,
 } from "@capakraken/shared";
 import { TRPCError } from "@trpc/server";
 import { z } from "zod";
@@ -24,7 +25,7 @@ export const allocationConflictProcedures = {
    * Read-only — no mutations.
    */
   checkConflicts: managerProcedure
-    .input(CheckConflictsInputSchema)
+    .input(CheckConflictsInputSchema as z.ZodType<z.infer<typeof CheckConflictsInputSchema>>)
     .query(async ({ ctx, input }): Promise<AllocationConflictCheckResult> => {
       const resource = await ctx.db.resource.findUnique({
         where: { id: input.resourceId },
@@ -39,8 +40,7 @@ export const allocationConflictProcedures = {
         throw new TRPCError({ code: "NOT_FOUND", message: "Resource not found" });
       }
 
-      const fallbackDailyHours =
-        (resource.country?.dailyWorkingHours ?? 8) * (resource.fte ?? 1);
+      const fallbackDailyHours = (resource.country?.dailyWorkingHours ?? 8) * (resource.fte ?? 1);
       const availability = (resource.availability as WeekdayAvailability | null) ?? {
         monday: fallbackDailyHours,
         tuesday: fallbackDailyHours,
@@ -82,7 +82,12 @@ export const allocationConflictProcedures = {
         input.endDate,
         input.hoursPerDay,
         availability,
-        existingAssignments as { startDate: Date; endDate: Date; hoursPerDay: number; status: import("@capakraken/shared").AllocationStatus }[],
+        existingAssignments as {
+          startDate: Date;
+          endDate: Date;
+          hoursPerDay: number;
+          status: AllocationStatus;
+        }[],
       );
 
       // Compute max overbook percentage for the worst day
@@ -90,9 +95,7 @@ export const allocationConflictProcedures = {
       for (const conflict of availabilityResult.conflicts) {
         const totalBooked = conflict.existingHours + conflict.requestedHours;
         const overbookPct =
-          conflict.availableHours > 0
-            ? ((totalBooked / conflict.availableHours) - 1) * 100
-            : 100;
+          conflict.availableHours > 0 ? (totalBooked / conflict.availableHours - 1) * 100 : 100;
         if (overbookPct > maxOverbookPercent) maxOverbookPercent = overbookPct;
       }