Grey shadows running through photo

Yes, manual correction is the only way to go.

What causes this is using silent/electronic/"rolling" shutter on a mirrorless camera. The sensor isn't read all at once, but instead scanned line by line. This causes interference patterns with the inherent flickering of LED lights.

The solution is to turn the mechanical shutter on when you know there's LED lighting - as you can with most mirrorless system cameras like Nikon Z, Sony alpha or Canon R - or at least avoid a certain shutter speed range (in the 1/100 to 1/400 range typically)

To remove this pattern of shadows and highlights, simply make 2 curves layers.

Use the first to lighten and the second to darken.

Lighten the shadow areas with a soft brush on a black mask.  Adjust the curves to accomplish the correct amount of lightening and darkening.  Use a very soft brush and an opacity about 30-40%

Although this image might not be exactly as you would expect it took about 5 mins to do, so put in the time required to perfect it and you will be able to use this method many times. 

Maybe some sort of Adjustment Layer with a striped Layer Mask?. You.d need a pattern of diffuse stripes, and you'd transform them to get the spacing and position right. It'd be a good idea to expand the Canvas horizontally first. Fortunately, a diffuse pattern will have less issues being scaled way up, if necessary [I measure the bands in your image as being about 311 pixels apart].

You'd have to set up the blending of the adjustment so that it would mostly affect the problem areas most. It might be necessary to run Curves on the mask, too, to get it to match the banding. This would have to be through Image > Adjustments, not an Adjustment layer, so you'd want to save various versions of the mask, in case you need to go back to a previous one.

You might also want to look around in the Premier Pro forum. As I was doing a quick search for "Fixing rolling shutter banding", most hits seemed to be about video, with references to Premier.