Jean-FrancoisHIVERT Thank you for noticing this.
Selecting $ together with the variable name is exected behavior. (In PHP $ is a part of the variable name token).
This can be configured using editor.wordSeparators setting (https://code.visualstudio.com/api/language-extensions/language-configuration-guide#word-pattern).
Search for the following setting "@lang:php editor.wordSeparators" in File / Preferences / Settings:

or put the following into your global settings.json:
"[php]": {
"editor.wordSeparators": "`~!@#$%^&*()-=+[{]}\\|;:'\",.<>/?"
}
Make sure, the editor.wordSeparators setting contains $- so it won't get selected when double-clicking.