Start: default search params not working properly with base paths configured #5477

Which project does this relate to?

Start

Describe the bug

I’m seeing some weirdness when a base path is configured with an app that has default search parameters via a zod schema.

Your Example Website or App

https://codesandbox.io/p/devbox/composed-middleware-typing-issue-1-132-7-forked-85dx8w

Steps to Reproduce the Bug or Issue

1. Visit repro url
2. Manually type in https://85dx8w-5173.csb.app/base/foo and press return to trigger load of /foo page
3. Observe it does not match the /foo route and shows a vite suggestion to visit /foo?search=query instead
4. Click on the link and observe the url doesn’t change, but the search params are populated and the page renders
5. Hit the reload button and see it redirect back to /base

Note: this happens in spa mode and regular mode

Expected behavior

I expect that visiting /base/foo should redirect me to the default search params specified by the schema (/base/foo?search=query)

Screenshots or Videos

Platform

• Router / Start Version: Start: 1.132.56; router: 1.132.47
• OS: macOS
• Browser: Chrome
• Bundler: vite
• Bundler Version: v7.1.10

Additional context

No response