Configure Filesystem Browser to show current project folder (analogous to behaviour of git window)

The behaviour of the git window is to "follow" the currently edited file, i.e. if the file belongs to a project, then open the project automatically. This is great.

I would like to configure the Filesystem Browser analogously, that is: open the project folder in the Filesystem Browser window automatically (if the file belongs to a project).

Is this currently possible? I did not see anything related in the browser's "configure" context menu. There is a "current document folder" entry, but this is cumbersome. First, I have to actively press the button (not automatic), and second, the files are often in a subfolder, and I almost never want to switch to the subfolder of a project, but instead to the project's parent folder.

I am used to this behaviour from VScode.

What would I have to do to implement this? Would this be best done with a plugin?

Thanks a lot for your help!