PhpStorm code completion doesn't show core classes/extensions

Solution 1:

I've solved the issue. File > Invalidate Caches did the trick!

Solution 2:

I had a problem with PHPStorm Code Analysis hanging up (never finishing) on certain files using certain classes. No errors were reported, but all code completion was not working in these problem files.

The solution was the same, File > Invalidate Caches.