I removed the fairing on my TLs for some maintenance and
noticed that the intakes scoop seems to float. No screws are missing
but it does move back and forth on the centre screw.
Is this normal or should it mount firm to the side of the fairing?
The side play is normal. It allows for a less than perfect alignment between the airbox location and the multiple fairing mounting points. If all the parts were rigidly bolted together, you can be sure there would be alignment issues - on some bikes more than others.