Vue + TS in single VS split file component

Hi to the community!

In our project we've moved from single to split file Vue components and I've stumbled onto a problem. When I write html templates directly in .vue files TS checks work perfectly fine:

But when I move the template out of .vue file and import it through 

<template lang="html" src="./view.html" />

TS checks and script property highlights do not work in templates anymore. 

I want to be able to see TS checks in my templates regardless of the file type (.vue or .html).

Have anyone encountered same kind of problem? How did you solve it or can it be solved at all?

Tech. details:

1. OS: MacOS Monterey (12.4)
2. WebStorm: 2021.3.2
3. Vue: 2.6.14
4. TS: 4.3.2
5. TSLint WS plugin: bundled 213.6777.57
6. Vue.js WS plugin: bundled 213.6777.57