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.
Answer from attdona on Stack OverflowVideos
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.
Well, like @user2982122 mentioned but instead of File go to Code -> Preferences -> Settings, then look for Quote, select Prettier and check both boxes

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.
This only happens if you have ' in your string e.g. ('it\'s a thing').
Prettier has this issue and there is apparently no solution to this.
My workaround is, using `` (string template syntax) for such strings and single quote for all other strings.
`it's a thing`
You don't have to escape this.