qgis - How to export a single feature (line) from multiple layers and export to individual layers?

I have multiple vector layers representing a time series. Each layer contains many lines each. I want to select a single specific line from each of these these layers and save it to another layer. This line represents the same feature (coastline) in every layer but it's position changes over time.

I can certainly do it 1 by 1 using "export - save selected features as...", but that would take forever. Also, I can't highlight all 40+ layers and use "Select Features by area" tool...

This is what 1 layer looks like:

This is all the layers with the info I want!