I don't have prettier extension installed, but after reading the possible duplicate answer I've added from scratch in my User Setting (UserSetting.json, Ctrl+, shortcut):

"prettier.singleQuote": true

A part a green warning (Unknown configuration setting) the single quotes are no more replaced.

I suspect that the prettier extension is not visible but is embedded inside the Vetur extension.

Use a Prettier configuration file in your project folder: .prettierrc

Inside your config file use Prettier overrides: https://prettier.io/docs/en/configuration.html#configuration-overrides

So in your case this example config should work (.prettierrc):

{
    "singleQuote": true,
    "overrides": [
        {
            "files": ["**/*.css", "**/*.scss", "**/*.html"],
            "options": {
                "singleQuote": false
            }
        }
    ]
}

In addition to @Barmar answer, you could also use prettier configuration on a .eslintrc.js file using the following, property:

rules: {
    // ...
    'prettier/prettier': ['error', { singleQuote: true }]
  }

As you already have singleQuote: true set in your prettier config, I suspect that you're seeing your single quotes converted to double quotes specifically inside your JSX tags. This is because Prettier has a separate rule for JSX:

"jsxSingleQuote": true

Without this, even with "singleQuote": true, Prettier will still convert single quotes within JSX to double.

According to Prettier, double quotes in JSX is the default because it's descended from HTML, where double quotes are more common.

Set "jsxSingleQuote": true wherever you have your Prettier config, and that should do the trick.