Apply .cube LUT
Load a 3D LUT and apply it with trilinear interpolation and adjustable strength.
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A 3D LUT maps input RGB to output RGB through a lattice, interpolating between the nearest eight lattice points. It can express white balance, exposure, curves, HSL and split toning — but nothing that depends on position. Sharpening, noise reduction, lens correction, cropping and any masked local adjustment are outside what a LUT can represent at all.
That limit is worth stating plainly, because "batch grading" is often assumed to mean "apply one LUT". A LUT is a delivery format for the colour part of a grade, not the grade itself. Use it after alignment, not instead of it.