I find I only really use three file extensions these days in Photoshop. The suggestion I have is simple an option in preferences to turn on or off all the "Save as" file extensions so I can just have the three I want so when I save as I don't have to.
This would be just a simple on/off check box system similar to turning "add-ons" on or off in the 3D modeling program Blender.
Or perhaps pressing a number key which can be hot keyed. For example I put in my file name for the project. Then at the bottom to change the file extension with the file type in selected in blue that I could press "1" , "2" or "3" which would be associated to a favored file extension so I can quickly do PNG instead of PSD.