When you say you've checked the wheel balancing, how many weights are needed to balance it?
I had a problem last year with my Landrover. Once over 50 it shook really badly. Had all 4 wheels balanced and 4 wheel geometry done but nothing really cured it. But it kept bothering me that 2 wheels took far too many weights to balance than I felt a newish car with top brand tyres should.
In the end, I resolved it with a brand new set of Pirellis. The old ones looked fine and passed the checks but clearly 2 of them weren't as round as they should have been. Probably as it had spent most of Covid sat around on them.
My XF was just a bit unpleasant at speed. Lots of vibrations, but very hard to pin down to a speed or scenario. I put it down to age but recently I had a blow out which was caused by a cracked alloy. As it was in the wheel refurb place I asked for all 4 to be checked for cracks and for straightness. Not surprisingly, for a car running 255/35/20's on pot holed roads, all 4 were out of shape. 1 weld, 4 straightens and 2 refurbs later and It's now a different car. Don't think it's ever driven so smoothly.
If the wheels are ok, then I'd be checking the brake disks.