The screen capture shows the white balance is "As shot" on the most selected image sync that will not achieve your expected result. Each selected image will just show the "As shot" for each individual image. Make a very small chang to the tint or temperature of the most selected image so that it shows as custom. That way you would be syncing the actual temp and tint values.
You haven't toggled 'Auto Sync', so Lightroom Classic will not sync anything until you click on the Sync button. And indeed, if your currently selected image is 'As Shot', then that is what all images will be if you do click 'Sync' and check the WB as one of the things to sync.