404 not found with `baseurl` configuration

[troubleshooting section]: https://vite-ruby.netlify.app/guide/troubleshooting.html

- [x] I have tried upgrading by running `bundle update jekyll-vite`.
- [x] I have read the __[troubleshooting section]__ before opening an issue.

### Description 📖

When `baseurl` in `_config.yml` is set, the server returns 404 error when It tries to get `/vite-dev`.

### Reproduction 🐞

1. clone [jekyll-vite-minima](https://github.com/ElMassimo/jekyll-vite-minima) repository
2. set `baseurl`
_config.yml:
```
baseurl: "/blog" # the subpath of your site, e.g. /blog
```
3. run `exe/dev` and open `127.0.0.1:4000/blog/`

Vite Ruby Info

_Run `bin/rake vite:info` and provide the output:_

```
Configuration file: /home/ksi/git/jekyll-vite-minima/_config.yml
bin/vite present?: true
vite_ruby: 3.9.1
jekyll-vite: 3.0.4
jekyll: 4.3.4
ruby: ruby 3.0.2p107 (2021-07-07 revision 0db68f0233) [aarch64-linux-gnu]
node: v20.7.0
npm: 10.1.0

installed packages:
jekyll-vite-minima@ /home/ksi/git/jekyll-vite-minima
├─┬ vite-plugin-ruby@3.0.3
│ └── vite@2.6.13 deduped
└── vite@2.6.13
```

### Logs 📜

_If not providing a reproduction:_

Output

_Run `DEBUG=vite-plugin-ruby:* bin/vite dev` or `DEBUG=vite-plugin-ruby:* bin/vite build` and provide the output:_

```
Configuration file: /home/ksi/git/jekyll-vite-minima/_config.yml
vite-plugin-ruby:config {
vite-plugin-ruby:config base: '/vite-dev/',
vite-plugin-ruby:config build: {
vite-plugin-ruby:config emptyOutDir: true,
vite-plugin-ruby:config sourcemap: false,
vite-plugin-ruby:config assetsDir: 'assets',
vite-plugin-ruby:config manifest: true,
vite-plugin-ruby:config outDir: '../.jekyll-cache/vite-dev',
vite-plugin-ruby:config rollupOptions: { input: [Object], output: [Object] }
vite-plugin-ruby:config },
vite-plugin-ruby:config root: '/home/ksi/git/jekyll-vite-minima/_frontend',
vite-plugin-ruby:config server: {
vite-plugin-ruby:config host: 'localhost',
vite-plugin-ruby:config https: false,
vite-plugin-ruby:config port: 3036,
vite-plugin-ruby:config strictPort: true,
vite-plugin-ruby:config fs: { allow: [Array], strict: true },
vite-plugin-ruby:config hmr: { host: 'localhost', port: 3036 }
vite-plugin-ruby:config },
vite-plugin-ruby:config entrypoints: {
vite-plugin-ruby:config 'entrypoints/application.js': '/home/ksi/git/jekyll-vite-minima/_frontend/entrypoints/application.js'
vite-plugin-ruby:config }
vite-plugin-ruby:config } +0ms

vite v2.6.13 dev server running at:

> Local: http://localhost:3036/vite-dev/
> Network: use `--host` to expose
```

_Also add any output from Jekyll._

### Screenshots 📷


Reproduce the issue in the jekyll-vite-minima example by setting baseurl in _config.yml, running exe/dev, and opening /blog/. Compare the Jekyll response with the bin/vite and DEBUG output; done means the Vite development endpoint loads correctly under the configured base path instead of returning 404.

Written by the indexing model from the issue text.