HTML and style/script formatting in Markdown

I'm writing Markdown files to generate static sites using VitePress. The VitePress library allows mixing HTML tags, JavaScript/TypeScript code, and CSS styles in a single .md file, similar to how we use the single-file component (SFC) format in Vue. However, it seems that HTML tags and code in <script> or <style> tags are not formatted. Would it be possible to add formatting for such blocks?

See also: https://vitepress.dev/guide/using-vue

Prettier 3.0.3
Playground link

--parser markdown

(I've tried the vue or html parsers as well, but they do not support Markdown syntax so the output is not correct either.)

Input:

---
hello:      world
---

<script setup>
import { ref } from 'vue'

const count = 
  ref( 0 )
</script>

## Markdown Content

The value for   `count`   is: {{ count }}

<div class="hello">
<span>Hello</span>
</div>

<style module>
.hello {
  color:      red
}
</style>

Output:

(The YAML front-matter formatting is correct.)

---
hello: world
---

<script setup>
import { ref } from 'vue'

const count = 
  ref( 0 )
</script>

## Markdown Content

The value for `count` is: {{ count }}

<div class="hello">
<span>Hello</span>
</div>

<style module>
.hello {
  color:      red
}
</style>

Expected behavior:

---
hello: world
---

<script setup>
import { ref } from 'vue'

const count = ref(0);
</script>

## Markdown Content

The value for `count` is: {{ count }}

<div class="hello">
  <span>Hello</span>
</div>

<style module>
.hello {
  color: red;
}
</style>

Start with the linked Prettier Playground and the provided Markdown input, comparing the current output with the expected output for script, HTML, and style blocks. Investigate the relevant Markdown formatting entry points and existing parser behavior for these embedded blocks. Done means the Markdown content, JavaScript or TypeScript, HTML, and CSS are formatted as shown while front matter remains correct.