`@clerk/nuxt` not work under `hash` router

[xdewx]

Preliminary Checks

• I have reviewed the documentation: https://clerk.com/docs

• I have searched for existing issues: https://github.com/clerk/javascript/issues

• I have not already reached out to Clerk support via email or Discord (if you have, no need to open an issue here)

• This issue is not a question, general help request, or anything other than a bug report directly related to Clerk. Please ask questions in our Discord community: https://clerk.com/discord.

Reproduction

https://there-no-need.com

Publishable key

pk_test_123

Description

Steps to reproduce:

1. install @clerk/nuxt module
2. set hashMode=true in nuxt.config.ts

router: {
    options: {
      hashMode: true,
    },
  },

2. set signInUrl & signUpUrl in nuxt.config.ts

  clerk: {
    signInUrl: "/sign-in",
    signUpUrl: "/sign-up",
    // afterSignOutUrl: "/sign-in",
    // signInForceRedirectUrl: "/",
  },

3. add pages sign-in & sign-up
4. add SignIn in /sign-in & add SignUp in /sign-up & SignInButton & SignUpButton in page header

Expected behavior:

everything is ok

Actual behavior:

1. SignIn & SignUp component is blank when open /sign-in & /sign-up
2. every click on SignInButton or SignUpButton will append ?redirect_url=xxx after current url, it will very long when click many times

Environment

prisma: ^7.7.0 => 7.7.0 
    sass-embedded: ^1.99.0 => 1.99.0 
    unocss: ^66.6.7 => 66.6.7 
    unplugin-auto-import: ^20.3.0 => 20.3.0 
    unplugin-icons: ^22.5.0 => 22.5.0 
    unplugin-vue-components: ^30.0.0 => 30.0.0 
    vue: ^3.5.32 => 3.5.32 
    vue-router: ^4.6.4 => 4.6.4