Drop the fork, remove the brake and crown race and inspect closely. More than one production fork has had little or no braze between the steerer and the crown, and check the region under the crown race.
If the fork checks out, check its alignment.
The metal rarely fails, the fabrication does from time to time.

A customer came into the shop once some 40 years ago complaining of brake shudder and a "loose" feel. Removed the wheel, removed the brake and the crown and blades fell to the floor. "There is your answer!"

I would also check the front wheel or better yet, take the easy way and exchange the front wheel and observe any difference.
Long ago, I experienced some speed wobble on a bike that had never presented it before. The wheel was 30 years old and at the time I built it up it was from all used parts save the nipples.
It was time to retire it. The rear I still cannot knock off... on that one I used CAD plated spokes not that you can tell that today.