The accepted answer is like chopping your arm off when your finger hurts! If you disable templateInterpolationService you lose a big part of the value of Vetur.

For me Vetur v0.35.0 broke when I upgraded typescript > 4.4

You can check which version(s) of typescript you're using by typing npm ls typescript in your project root.

If you're running typescript 4.4.4 (or lower), try this:

Restart Vue Lanaguage Server (in VSCode):
View ->
   Command Palette.. ->
      Vetur:Restart VLS (Vue Language Server)

If you're running typescript 4.5 or higher, you will probably run into this error. Still working to find a fix in this case.

Alternatively, to force your environment to use an older version of typescript across the board, you can ensure your version of npm is 8.3+ and use the new "overrides" section of package.json:

...
  "overrides": {
    "typescript": "4.4.4"
  },
...

So it turned out that this was because of Vetur experimental templateInterpolationService property. By turning it to false in the vetur.config.js file:

module.exports = {
  settings: {
    /* .. */
    'vetur.experimental.templateInterpolationService': false
    /* .. */
  }
};

Vetur stopped the unexpected interference with my components.

Making sure the gloabal ts version of vscode <=4.4.4. It may be some dependences(like @microsoft/api-extractor) using a newer typescript .

Creating vetur.config.js. Setting "vetur.useWorkspaceDependencies": "false" in settings. example:

module.exports = {
    settings: {
        "vetur.useWorkspaceDependencies": false,
        "vetur.experimental.templateInterpolationService": true
    }
}

Checking vscode OUTPUT panel in Vue Language Server, may:

[INFO ] Find node_modules paths in xxxxxxx - 247ms
[INFO ] Loaded bundled typescript@4.4.4.
[INFO ] Loaded bundled prettier.
[INFO ] Loaded bundled @starptech/prettyhtml.
[INFO ] Loaded bundled prettier-eslint.
[INFO ] Loaded bundled prettier-tslint.
[INFO ] Loaded bundled stylus-supremacy.
[INFO ] Loaded bundled @prettier/plugin-pug.

Success!