Syncing label colors between timeline and project panel

Sometimes I want to lable a clip in my project and want to see that same label also in the timeline.

In Premiere we have a switch for that ("show name and lable of the source clip") which switches between timeline and source label:

(sorry, at the moment I just have German UI)

In After Effects, we are able to switch between layer and source name by clicking on the column header:

but there is no way to do the same for the label.

This would be a nice addition for the labeling in After Effects.