URL search params aren't cleared on navigation with hash-based router

Describe the bug

When using router.type === 'hash', typical navigations via href="#/..." don't clear search parameters in the same way that their pathname counterparts do.

Reproduction

Use the search bar in https://github.com/stephenlrandall/kit-inline-test and then return to the home page.

Logs

System Info

System:
    OS: macOS 15.2
    CPU: (16) x64 Intel(R) Core(TM) i9-9880H CPU @ 2.30GHz
    Memory: 401.48 MB / 16.00 GB
    Shell: 5.9 - /bin/zsh
  Binaries:
    Node: 20.8.0 - /usr/local/bin/node
    npm: 10.1.0 - /usr/local/bin/npm
    pnpm: 9.15.4 - ~/Library/pnpm/pnpm
  Browsers:
    Chrome: 131.0.6778.265
    Edge: 131.0.2903.147
    Safari: 18.2
  npmPackages:
    @sveltejs/adapter-auto: ^3.3.1 => 3.3.1 
    @sveltejs/adapter-static: ^3.0.8 => 3.0.8 
    @sveltejs/kit: ^2.15.3 => 2.15.3 
    @sveltejs/vite-plugin-svelte: ^4.0.4 => 4.0.4 
    svelte: ^5.18.0 => 5.18.0

Severity

serious, but I can work around it

Additional Information

A workaround is to prepend all links without search params with ?#/..., although this is obviously undesirable.

Reproduce the issue using the linked kit-inline-test project with the hash-based router and a search-bar navigation. Start by tracing hash-router handling for href="#/..." versus pathname navigation; done means returning home clears the URL search parameters without requiring the ?#/... workaround.