Do you need to re-sharpen after "Export As"

Oh - obviously you wouldn't reopen an already saved jpeg to sharpen it. You downsample, sharpen, and then Export to jpeg.

»Does any think in todays high resolution images that sharpening after export on a JPG would be bad idea as it would lead to re-saving the JPEG again.«

Also you would be sharpening a JPG-damaged image, so possibly aggravating the artefacts. 

Lossy compression should, if used at all, be the last step. 

In principle one could speak of three »kinds« of sharpening in image editing: 

• Input Sharpening (usually in RAW development)

• Creative Sharpening (whatever you feel like improves the image basically)

• Output Sharpening (at final output with consideration of the actual process, not necessarily up to the photographer)

But how much time and energy you invest in either is up to you. 

Downsampling softens all edges, so I always sharpen after resizing. Not a lot, just enough to bring back the crisp edges.

Bicubic Automatic/Sharper is supposed to take care of it by including automatic sharpening in the algorithm. The problem is that a lot of us feel it's overdoing it, giving the result a coarse, oversharpened look. I consistently use Bicubic Smoother, which doesn't sharpen, and then run the ACR filter for sharpening afterwards. I find this superior to the old Unsharp Mask (or High Pass/Overlay which it's built on). You can use the Detail slider in the ACR filter to control halos.