This is a setup I’ve been looking at and I use the same two apps. A lot. Can you tell if the eGPU is making a decent difference in PS and LR? Do you have a dedicated scratch?
Coming from a film background, I don't take a lot of photos during a session, I try to get things right in the camera and I don't bother with trying to salvage problematic photos. This means that I do very basic editing in Photoshop/Lightroom. I don't use a lot of layers and I don't do batch processing. For my purposes, and having tested it, I think that an i5 mini and the integrated graphics work just fine.
I don't use a scratch disk because I've yet to see a need for one, especially since I have flash drives on both the mini and my iMac.
If have an i7 mini and an external video card for reasons that have nothing to do with still photography.
That said, there are people who are using an external video card with photo editing software whose needs are more demanding than mine and who find it useful. Have a look at post #149 in this thread, in which
@stillcrazyman talks about the benefit that he's getting from an external card.
Adobe has published support documents on how Photoshop/Lightroom use a GPU. Maybe have a look at these to help you decide whether an external GPU is worth the investment.