Getting intellisense errors when declaring or using TS types/interfaces in Vue.js SFC files

I'm developing a component for my Nuxt 3 project. I'm trying to declare an interface to provide strong typings for the component props, e.g.:

<script setup>
interface Props {
  float: number;
}

const props = defineProps<Props>();
</script>

However, VS Code's intellisense displays an error when I try to do so:

'interface' declarations can only be used in TypeScript files. ts(8006)

I also noticed it displays another error when I try to use any type annotations (e.g.: let x: string):

Type annotations can only be used in TypeScript files. ts(8010)

I could use runtime declaration syntax for the props - e.g.:

const props = defineProps({
  float: { type: Number, required: true },
});

But I'd rather use TypeScript syntax, as I want type safety and notation to be enabled project-wide.

What I've tried

I followed the standard steps to enable TS syntax for Vue files in VS Code:

• I have Volar installed;
• I also disabled the built-in TypeScript VS Code extension for the workspace in order to enable Takeover mode. The (takeover) label shows up in the status bar, indicating that it's working.

But it doesn't work. I tried restarting the Volar Vue Server, or even restarting VS Code altogether, but the errors persist. What could be causing the errors to appear?

Argh, noob mistake - I forgot to provide the lang="ts" attribute to the script tag:

<script setup lang="ts">
interface Props {
  float: number;
}

const props = defineProps<Props>();
</script>

After adding lang="ts", the problem is gone.

The most frustrating thing is that nowhere it's hinted from VS Code that its absence could be the cause of the errors and it looks as if Volar is simply not taking over. I only noticed it after taking another look at the docs.