Unfortunately, this feature is not currently available in VS Code. However, it has been added as a feature request for upcoming updates. You can track the issue on Github.
In the latest version of VS Code the IntelliSense in comments and strings have been disabled by default. Below are the two options to bring back "24/7 IntelliSense" functionality or customize it to your own liking.
First make sure you have installed the HTML CSS Support Extension mentioned by dwonisch above.
Control + ',' to go to settings or click File -> Preferences -> Settings.
Click workspace settings tab and enter the following JSON code:
{
"editor.quickSuggestions": {
"comments": false, // <- no 24x7 IntelliSense in comments
"strings": true, // but in strings and the other parts of source files
"other": true
}
}
The other option is to hit ctrl + space within the CSS quotes to activate the intelliSense. Example: