Hi, I am starting my journey to contribute to Blender and got curious about this issue as it would help me understand the inner working of nodes. I have recreated this issue and have been going through the code.
From my understanding the File Output node's preview should behave in the same way as Viewer node does. In COM_OutputFileNode.cc, I see converter.addNodeInputPreview being used the same way as in the COM_ViewerNode.cc but it doesn't seem to work in the former. In the Viewer node we are passing just the image socket to it, while in File Output node we are looping through and passing the inputs. Is this what should be done if we have just Png format instead of OpenEXR and there is only one input image socket?
I need to go a bit deeper into NodeConverter class and NodeOperation. The code comments do help but where can I find more about them.

Hmm a bit of a one off issue.

File output node is only executed when doing final composite.
Previews are only updated when editing.

This could be changed by changing the OutputFileNode::convertToOperations

if (!context.isRendering()) {

In file node_edit.c in method compo_startjob() we set value of rendering, and use it in OutputFileNode::convertToOperations, that is why

if (!context.isRendering()) {
}

is false in all cases.