How to Batch Save Layers in Photoshop

There is an option to save each layer as its own image in Photoshop, which is very useful if each layer is its own complete image.

File > Export > Layers to File

However, if, for example, we have lots of text layers we wish to save, all with the same background/foreground (see below), or we have lots of different icons we want to save all with the same background, this is not sufficient.

Example of text layers with the same BG
If we use the Layers to File optio...