From the extension's page:

Features:

- Auto-installation: When you launch Claude Code from within VSCode’s terminal, it automatically detects and installs the extension

- Selection context: Selected text in the editor is automatically added to Claude’s context

- Diff viewing: Code changes can be displayed directly in VSCode’s diff viewer instead of the terminal

- Keyboard shortcuts: Support for shortcuts like Alt+Cmd+K to push selected code into Claude’s prompt

- Tab awareness: Claude can see which files you have open in the editor

- Configuration: Set diff tool to auto in /config to enable IDE integration features

It was slightly buggy it was uninstalled itself sometimes. I hope this will be better now with this official extension

So I won't get anything more that the file compare that appear when claude in terminal ask to modify a file ?

You can select lines, which will be added to the context (can't do that from the console), it can show the edited files in the VSCode editor, not just in the terminal.

The extension say "Tab awareness: Claude can see which files you have open in the editor" I don't know how to activate this, it would help me to not have to CD in the terminal each time

Ok so I tested it by CD into a directory, and open a file from another directory, create an empty function and selecting the function in the editor, and asking claude to just "fill the function" it knew which text was selected in which file and filled the function, this will gain me some time