Updating search params via a <Link> does not work on the first click if a declarative route mask is used

Describe the bug

When using a <Link> component, I expect that using the search prop would update the search parameters in the URL whenever I click the <Link>.

For example, the code snippet below should increment the page search param in the URL whenever clicked.

<Link search={(prev) => ({ ...prev, page: (prev.page ?? 1) + 1 })}>Click me<Link />

This works great.

However, when I add a route mask to the router, the search parameters no longer update on the first click.

const maskSearchUserId = createRouteMask({
  routeTree,
  search: (prevSearch) => {
    const newSearch = { ...prevSearch };
    delete newSearch.userId;
    return newSearch;
  },
});

// Create a new router instance
const router = createRouter({
  routeTree,
  routeMasks: [maskSearchUserId],
});

For reference, here is the search param setup:

import { Link, createRootRoute } from '@tanstack/react-router';
import z from 'zod';

const searchSchema = z.object({
  userId: z.coerce.string().min(1).optional().catch(undefined),
  page: z.coerce.number().min(1).catch(1),
});

export const Route = createRootRoute({
  validateSearch: searchSchema,
  ...
});

Your Example Website or App

https://stackblitz.com/edit/github-rbjvhp?file=src%2Froutes%2F__root.tsx

Steps to Reproduce the Bug or Issue

1. Go to the StackBlitz link provided
2. Open the StackBlitz preview in a new tab via the "Open Preview in new tab" button so you can view the URL as it updates
3. Click once on the "Click to increment page search param" link and observe the URL does not change.
4. Click a second time on the "Click to increment page search param" link and observe the URL search params do change from ?page=1 to ?page=2.

Expected behaviour

As a user, I expected the URL search params to update whenever I clicked on a <Link> that updates the search parameters.

Screenshots or Videos

Here's a demo where I click on the <Link> twice, a few seconds apart.

Notice how the URL only updates the second time.

https://github.com/user-attachments/assets/671b5fe3-d8a7-4970-9022-4902f32cc784

Platform

• OS: macOS
• Browser: Chrome
• Version 127.0.6533.89 (Official Build) (arm64)

Additional context

• Removing the route mask resolves the issue.
• Supplying a "dummy" route mask (below) that passes the previous value through does not resolve the issue.

search: (prev) => {
    return prev;
},

Reproduce the first-click behavior from the linked StackBlitz example, then trace navigation from the search prop through createRouteMask and createRouter. Done means the masked route updates the URL search parameters on the first click, while the existing behavior without a mask remains intact.