You can't really do that, the closest you can get is changing a connection color/style and applying that to all up- and/or downstream connections, but that will highlight all connections that features from that specific connection can theoretically pass through.

Add an attribute at the beginning of the workspace, and append some meaningful text to that attribute in every branch your feature may pass through. Unfortunately this will not show the path on the canvas, but the attribute will show you the path each individual feature followed.

You may want to upvote this idea.

Thanks for the answers. I voted for the good idea ^^